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A deformable robot is a new type of robot that utilises a metamorphic mechanism into the field of robotics and switches between vehicular and humanoid states during reconstruction processes. In the process of driving reconstruction of the deformable robot, the nonlinear vibration will be generated due to the excitation of uneven roads, and tipping instability of the deformable robot may occur. To address this phenomenon, the effect of road excitation on the stability of the deformable robot during driving reconstruction process was investigated based on a nonlinear dynamics analysis method. In this study, a kinematic model for the coupled reconstruction process of a deformable robot was developed using the homogeneous coordinate transformation method. A nonlinear dynamics equation for the variable-centre-of-mass system of the robot was derived for the driving reconstruction process. Nonlinear dynamics analysis methods were applied to analyze the nonlinear response and the change of the system stability of the deformable robot driving reconstruction under the influence of different road excitation amplitudes, excitation frequencies, and reconstruction speeds. The accuracy of the established nonlinear dynamics model was further verified through experiments. It is shown that when the road excitation amplitude exceeds 0.07 m or the excitation frequency exceeds 7.2 Hz , irregular chaotic motion as well as tipping instability may occur. With the increase of reconstruction time, the stability of the deformable robot is enhanced during driving reconstruction. When the reconstruction time exceeds 18 s, the driving reconstruction of the deformable robot can be stably executed on typical roads. [ABSTRACT FROM AUTHOR]

Vortex-induced vibration (VIV) of large-span cables has become a significant engineering problem to be solved. As a typical continuous body with quadratic and cubic nonlinearity, the modal resonance of the cable has a great effect on its dynamics, especially with the fluid–structure interaction. The nonlinear dynamic behaviors of multiple modal VIV of a cable are studied in this paper with the combination of theoretical perturbation method and numerical simulation of Computational Fluid Dynamics (CFD). Firstly, motion equations for the cross-flow vibration of the cable under uniform airflow are established, van der Pol wake oscillator is used to simulate the fluid load caused by the vortex shedding. Galerkin's method is utilized to discretize the partial differential equations into reduced ordinary differential equations. Secondly, modulation equations with 2:1 internal resonance of the cable are derived by the method of multiple scales. Frequency–response curves of the system are plotted and validated by the Runge–Kutta method, where the necessary aerodynamic coefficients for the perturbation analysis are supplied by solving the corresponding two-dimensional (2-D) CFD model based on the Shear Stress Transport (SST) k–ω model. Finally, the parametric influence of structural, aerodynamic, and coupling parameters on the nonlinear dynamic behaviors is explored. Results novelty reveal the bending of the frequency response curve due to structural geometric nonlinearity and nonlinear damping of the wake oscillator is tightly related to the 'lock-in' phenomenon. Variation of structural and aerodynamic parameters will significantly change the 'lock-in' domain. The low-to-high and high-to-low frequency sweeps have different 'lock-in' domains. The jump phenomenon occurs at the endpoints of the 'lock-in' domain. [ABSTRACT FROM AUTHOR]

During the COVID-19 pandemic, many countries face healthcare system collapses, then leading governments to recognize the importance of rational allocation of limited medical resources. Therefore, we construct an epidemic propagation model on a meta-population network using the microscopic Markov chain method. Unlike other works, our model accounts for nonlinear recovery rates due to healthcare system collapse and resource limitations. Combining Monte Carlo simulation, we analyze the impact of medical resources on the phase transition, steady state infected density and propagation threshold of disease spread. An interesting finding is that when medical resources are severely limited, allocating resources to smaller cities can most effectively contain the epidemic. Furthermore, it is found that introducing a healthcare system collapse mechanism results in two propagation thresholds, rendering the outbreak of epidemics to be dependent on the initial proportion of infected individuals. Finally, we validate our results on the constructed real population network. [ABSTRACT FROM AUTHOR]

Due to scale effects, micromechanical resonators offer an excellent platform for investigating the intrinsic mechanisms of nonlinear dynamical phenomena and their potential applications. This review focuses on mode-coupled micromechanical resonators, highlighting the latest advancements in four key areas: internal resonance, synchronization, frequency combs, and mode localization. The origin, development, and potential applications of each of these dynamic phenomena within mode-coupled micromechanical systems are investigated, with the goal of inspiring new ideas and directions for researchers in this field. [ABSTRACT FROM AUTHOR]

A granular damper consists in a container partially filled with solid particles that attenuate vibrations thanks to the multiple dissipative particle–particle collisions. These dampers have been investigated for decades because they are affordable, require low maintenance and can operate in harsh environments where viscous dampers fail. However, the nonlinear response of granular dampers, which includes chaotic dynamics and sharp transitions in loss factor, makes it difficult to predict their final performance when attached to the primary vibrating structure. To some extent, this has hampered widespread utilization of granular dampers in the industry. We show that a cone-in-cone design of such dampers can lead to an essentially linear response, which is compatible with a simple force law. [ABSTRACT FROM AUTHOR]

Real-world multibody systems do not have ideal joints; most joints have some clearance. The clearance allows the connected bodies to undergo a misalignment, and the resulting dynamics is governed by the contacts thus formed. Two approaches are typically taken to deal with contacts: the commonly used continuous dynamics approaches assume the Hertzian nature of the contact modeled by nonlinear unilateral spring-damper elements; while the nonsmooth dynamics approach results in a complementarity problem. This paper employs a nonsmooth dynamics approach to develop a coherent framework for the simulation of multibody systems having frictionless joints with clearances. Because clearances are of small magnitude relative to the dimensions of the mechanical components, the nature of the contact in the joints is assumed to be inelastic. Using this assumption and the general nonsmooth dynamics framework, the parametric formulations for cylindrical, prismatic, and revolute joints with clearances are derived. The equations of motion are formulated, and their time-discretized counterparts are cast as a nonlinear programming problem. The proposed scheme also enforces normalization constraint on Euler parameters in contrast to state-of-the-art methods that is conducive to stability of the solution for a suitable range of step sizes. In addition, a variable time-stepping scheme that includes the step size as an extra variable in the optimization is introduced and its stability properties are discussed. The versatility of the proposed framework is demonstrated through numerical experiments. [ABSTRACT FROM AUTHOR]

Understanding the mechanisms of oscillatory behavior is an important issue in modern nonlinear dynamics. We study stochastic excitation of complex oscillations in a nonlinear dynamic model of thermokinetics. A wide diversity of mono- and bi-stability regimes in the deterministic version of this model is demonstrated. For the model that takes into account multiplicative stochastic disturbances, underlying mechanisms of transformations of equilibrium modes into the large-amplitude spiking oscillatory regimes are clarified. We study in detail scenarios of stochastic excitement with the help of direct numerical simulations and analytical stochastic sensitivity technique. The work demonstrates the constructive capabilities of geometric analysis of the relative positions of separatrices and confidence ellipses. [ABSTRACT FROM AUTHOR]

Achieving accurate daily runoff predictions in data-scarce regions is challenging. This paper presents an improved anticipated learning machine (IALM) based on nonlinear dynamics. The IALM leverages both the spatial information among runoff stations and the temporal information within runoff sequences, achieving precise runoff prediction. First, temporal information is extracted through a convolutional neural network (CNN). Second, spatiotemporal information is fused through an artificial neural network (ANN). Third, the mapping between the nondelay and delay attractors is simulated by an anticipated learning neural network. Using daily runoff sequences from 107 stations across the United States as input, the performance of the IALM is evaluated at eight stations for training sample sizes ranging from 300 to 70. Compared with the ALM, autoregressive neural network (ARNN), and three deep learning models (self-attentive long short-term memory [SA-LSTM], temporal convolutional network (TCN), and long- and short-term time-series network [LSTnet]), the IALM maintains high predictive accuracy and stability as the number of training samples decreases. The IALM method consistently captures runoff trends, accurately predicts runoff peak points, and overcomes challenges associated with time lag and low accuracy under small sample conditions. Moreover, in comparison to the ALM, the IALM significantly enhances the predictive accuracy, achieving R and Nash–Sutcliffe efficiency (NSE) indices of 0.9 for multiple stations. At the USGS 01013500 station, the NSE value of the IALM improves by 127.71–252.93% when using only 100 training samples, while the NSE value of the LSTnet decreases to approximately 0 under the same conditions. When 70 training samples are used, the IALM achieves an R improvement of 21.17–47.66% relative to the ALM and the three deep learning models. Compared with the ARNN at eight sites, the IALM maintains superior prediction performance at each site, while the ARNN performs well at only a few sites and average at most sites, with unstable prediction performance. The results show that IALM, based on nonlinear dynamics, effectively incorporates and exploits spatiotemporal information from short-term high-dimensional data, compensating for limited sample lengths. Therefore, IALM provides a novel methodology for runoff prediction in data-scarce regions. [ABSTRACT FROM AUTHOR]

This paper describes the experimental campaigns on the Tower of the Palazzo dei Vicari in Scarperia, a village in the Mugello area (Tuscany) exposed to high seismic hazards. The first campaign was carried out from December 2019 to January 2020, and the Tower underwent the so-called Mugello seismic sequence, which featured an M 4.5 earthquake. Other ambient vibration tests were repeated in June 2021 and September 2023 when another seismic sequence struck the area near Scarperia. These tests aimed to characterise the Tower's dynamic behaviour under ambient and seismic excitations and check the response of the Tower over time. The experimental results were then used to calibrate a finite-element model of the Tower and estimate its seismic vulnerability. Several numerical simulations were conducted on the calibrated model using the NOSA-ITACA code for nonlinear structural analysis of masonry buildings. The dynamic behaviour of the Tower subjected to a seismic sequence recorded in 2023 by a seismic station at the base was investigated by comparing the velocities recorded along the Tower's height with their numerical counterparts. Furthermore, several pushover analyses were conducted to investigate the collapse of the Tower as the load's distribution and direction varied. [ABSTRACT FROM AUTHOR]

Over the past two decades, data-driven reduced-order modeling (ROM) strategies have gained significant traction in the nonlinear dynamics community. Currently, several challenges in physical interpretation and data availability remain overlooked in current methodologies. This work proposes a novel ROM methodology based on a newly proposed generalized characteristic value decomposition (GCVD) to address these obstacles. The GCVD-ROM approach proposes a new perspective toward data-driven ROMs via characterization of the dynamics before any ROM considerations are made. In doing so, a significant degree of versatility is inherited in the GCVD-ROM strategy, allowing our models to reproduce the full-scale dynamics in different regions of the parameter space at the cost of a single training data set. Our approach utilizes computationally efficient free-decay data sets alongside a windowed-decomposition scheme, allowing us to extract energy-dependent modal structures for use in model-order reduction. This is accomplished using the physically insightful characteristic values provided by the GCVD, which are shown to be directly related to the system poles at a particular response amplitude. This natural metric, paired with a resonance tracking scheme, allows us to address the difficulties associated with physical interpretation and data availability without sacrificing the convenient aspects of linear projection-based model order reduction. A computational framework for the continuation and bifurcation analysis using linear projection-based ROMs is also presented, permitting us to deploy rigorous analysis and bifurcation studies to verify that our ROMs reproduce the intrinsic complexity of full-scale systems. A detailed walk-through of the GCVD-ROM approach is demonstrated on a simple system where important practical considerations and implementation details are discussed using a concrete example. The discretized von Kármán beam and shallow arch partial differential equations are also used to explore complicated scenarios involving modal coupling across disparate time scales and internal resonances. [ABSTRACT FROM AUTHOR]

Purpose: In this study, we investigate the minimum time (MT) for the spatial motion of a free rigid body (RB) under the influence of viscous friction and gyrostatic moments (GMs). Assuming that the body’s center of mass coinciding with the original point of two Cartesian systems of coordinates. Results: The optimal control (OC) law for the slow movements, as a main goal, is established, and the corresponding time and phase pathways are assessed. Conclusion: The resulting innovative outcomes are achieved and displayed for two new scenarios in various graphs to show the gyrostatic moment’s positive impacts. When comparing the obtained results with the previous one when the gyrostatic moment isn’t present, amazing consistency is observed, and the slight deviations between them are discussed. As a result, the acquired results generalize those that were discovered in earlier investigations. Applications: The significance of this study arises from its practical implications in everyday existence, that confine themself to applying gyroscopic theory to preserve the stability and balance of vehicles in the design of which gyroscopes are used, in addition to determining the path of aircraft and marine vehicles. [ABSTRACT FROM AUTHOR]

Purpose: The bidirectional gear-driven friction nanogenerator can convert mechanical energy into electrical energy through transmission system and energy acquisition technology, which is of great significance in the development of miniaturization, intelligence and greening. Therefore, this study aims to explore the relationship between the dynamic characteristics of mechanical transmission system and the mechanical energy conversion efficiency of bi-directional gear-driven friction nanogenerator system. Methods: Considering the time-varying mesh stiffness, time-varying support stiffness, transmission error, tooth side clearance and bearing clearance, the nonlinear dynamic model of the mechanical transmission system of the bidirectional gear-driven friction nanogenerator is established. The Runge Kutta method was used to solve the vibration differential equation of a mechanical transmission system, and the influence of external load excitation frequency on the dynamic characteristics of the system was analyzed. The influence mechanism of external load excitation frequency and average mesh stiffness on the mechanical energy harvesting of the system was analyzed by combining the friction nanogenerator (TENG) energy harvesting technology. Results: There are abundant nonlinear phenomena in the mechanical transmission system of bi-directional rack-driven friction nanogenerator. With the increase of the external load excitation frequency and the average meshing stiffness, the vibration characteristics of the mechanical transmission system will experience three different motion states, the power generation of the system will increase, but the mechanical energy conversion efficiency of the system will decrease. Conclusions: The results show that the mechanical energy conversion efficiency can be improved and the power generation of TENG can be increased by reasonably selecting the external load excitation frequency and meshing stiffness and avoiding the unstable region. [ABSTRACT FROM AUTHOR]

Purpose: To explore the impact of gear floating on the system's nonlinear dynamic characteristics, a gear floating model was developed based on the concept of gear floating. Methods: A nonlinear dynamic model, bending-torsional-axial-pendular (BTAP), has been developed for a coaxial reverse closed differential herringbone gear transmission system (CRCDHGTS), accounting for gear floating. This model considers factors such as gear floating backlash, tooth surface friction, gyroscopic effects, time-varying meshing stiffness (TVMS), meshing damping, and dynamic meshing parameters. A calculation model for the floating backlash and floating TVMS of a herringbone gear system was derived, and the nonlinear dynamic response of the gear system was solved using the Runge–Kutta method. Results: The influence of input speed, initial backlash, gear float value, and system transmission error on the nonlinear dynamic vibration characteristics is analyzed using various diagrams, including bifurcation diagrams, maximum Lyapunov exponent (MLE) plots, time history diagrams, frequency diagrams, phase diagrams, and Poincaré section diagrams. Conclusions: The research reveals that gear floating diminishes the chaotic motion behavior of the system under different excitation factors, thereby improving the system's global bifurcation characteristics. The developed BTAP coupled nonlinear dynamic model provides more accurate numerical solutions compared to models with fixed meshing parameters, rendering it more suitable for analyzing the system's dynamic characteristics. Analysis of the gear floating value indicates an optimal range of 0–20 μm and 34–43 μm for generating periodic motion, with floating values around 10–20 μm demonstrating better performance in mitigating the negative effects of initial backlash and transmission error. [ABSTRACT FROM AUTHOR]

Purpose: Numerous structural parameters of rotor systems in engineering machinery are subject to uncertainties. For instance, parameters like the eccentricity and phase of aircraft engines and gas turbines show considerable variations and uncertainties, complicating the evaluation of the system’s dynamic characteristics. Methods: To investigate the influence of uncertain parameters on the vibration characteristics of a multi-disk rotor-bearing system, this study considers several factors including the deformation of bearing seats, Hertzian nonlinearity, clearances, eccentricity, and initial phase. A nonlinear dynamic model of a three-disk rotor-bearing system is established, and the numerical vibration responses were compared with experimental data to validate the effectiveness of the model. The impact of uncertain parameters on the system is investigated using the Monte Carlo method. Results: The results indicate that uncertain parameters, such as eccentricity, phase difference, and bearing clearance, have a significant impact on the vibration behavior of the system, particularly on the second-order resonance and non-resonance intervals of the system. Therefore, it is important to pay attention to the influence of these parameters on the vibration of rotor-bearing systems in high-speed rotating machinery equipment. [ABSTRACT FROM AUTHOR]

The focus of this paper is to examine the motion of a novel double pendulum (DP) system with two degrees of freedom (DOF). This system operates under specific constraints to follow a Lissajous curve, with its pivot point moving along this path in a plane. The nonlinear differential equations governing this system are derived using Lagrange's equations. Their analytical solutions (AS) are subsequently calculated using the multiple-scales method (MSM), which provides higher-order approximations. These solutions are considered new, as the traditional MSM has been applied to this novel system for the first time. Additionally, the accuracy of these solutions is validated through numerical results obtained using the fourth-order Runge–Kutta method. The solvability conditions and characteristic exponents are determined based on resonance cases. The Routh–Hurwitz criteria (RHC) are employed to assess the stability of the fixed points corresponding to the steady-state solutions. They are also used to demonstrate the frequency response curves. The nonlinear stability analysis is performed by examining the stability and instability ranges. Resonance curves and time history plots are presented to analyze the behavior of the system for specific parameter values. The investigation delves into a comprehensive analysis of bifurcation diagrams (BDs) and Lyapunov exponent spectra (LEs), aiming to uncover the various types of motion present within the system. Systematic examination of these charts reveals critical insights into transitions between stable, quasi-stable, and chaotic dynamical behaviors. This work has practical applications in various fields, such as robotics, pump compressors, rotor dynamics, and transportation devices. It can be used to study the vibrational motion of these systems. [ABSTRACT FROM AUTHOR]

Purpose: This research introduces an innovative solution that revolutionizes the study of linear and nonlinear dynamical systems—a smart automatic modal hammer. With its affordability and intelligent capabilities, this automatic modal hammer becomes an invaluable tool for research and industry, enabling repeatable strikes with precise force control. This system's significance becomes particularly evident when studying nonlinear systems, which heavily rely on the excitation level for their dynamics. By offering a cost-effective design this proposed system proves to be robust in accelerating research on nonlinear dynamics, providing researchers with an efficient and accessible means to delve deeper into these complex systems. Methods: The proposed design integrates a commercial modal hammer, commonly used in modal testing, and a stepper motor. This stepper motor is enhanced with an encoder and servo driver, all expertly controlled by a Raspberry Pi. Results: What sets this system apart is its clever utilization of regression models to acquire knowledge of the intrinsic relationship between the applied force and hammer velocity precisely during the impact. This acquired knowledge is the foundation for controlling the motor's behavior, ensuring consistent and accurate excitation of the structure with the desired force. Conclusion: The capabilities of the proposed automatic modal hammer are demonstrated using a linear two-story tower and a model airplane wing with a nonlinear vibration absorber. [ABSTRACT FROM AUTHOR]

Purpose: Investigating the nonlinear dynamic response of giant magnetostrictive actuator (GMA) is a valuable subject in the field of precision engineering. In order to effectively control the nonlinear dynamic response of a single-degree-of-freedom GMA, a fractional-order time-lag feedback controller is designed. Methods: We model the nonlinear dynamics of the controlled GMA through the geometric nonlinearity imposed by the disc-spring mechanism and introduce the dimensionless for simplification. The flexible order adjustment capability of the Riemann–Liouville fractional-order derivatives is adopted to more accurately simulate the memory effects and nonlocal properties of the system. It effectively compensates its nonlinear dynamic behavior to optimize the system design and control. By using the averaging method, the amplitude–frequency response equations of the primary resonance in the system containing a fractional-order time-lag feedback control strategy are solved and the stability conditions are obtained. Results: Through detailed parametric studies, the effects of key structural parameters within the uncontrolled GMA and the adjustment of the parameters under fractional-order time-lag feedback control on the primary resonance response characteristics are researched. Moreover, the time-lag feedback gain and fractional-order are adjusted to effectively guide the system into the desired chaos, or to get the system out of the chaotic state and back to a stable periodic behavior. Conclusions: The research results show that the unstable region of the primary resonance curve can be significantly reduced or eliminated by choosing suitable adjustment parameters, so as to better realize accurate and reliable motion control. [ABSTRACT FROM AUTHOR]

A third-order shear deformation beam model for nonlinear dynamic analysis of a two-directional functionally graded (2D-FG) beam under a moving load is presented. Distinct from the existing higher-order beam models, the present model employs the transverse shear rotation rather than the cross-sectional rotation as an independent variable. The material properties are continuously varied in both the axial and thickness directions by power distribution laws, and they are estimated by four homogenization schemes, namely the schemes due to Voigt, Mori–Tanaka, Hashin–Shtrikman and Reuss. A beam element is derived and used to transfer the nonlinear differential equation to a discretized form. Nonlinear dynamic response of the beam is predicted by the Newmark method in conjunction with Newton–Raphson iterative procedure. Numerical results reveal that the derived beam element which ensures a quadratic variation of the moment in axial direction is capable of furnishing accurate nonlinear dynamic characteristics with a smaller number of elements as compared to the one based on the conventional cross-sectional rotation. It is shown that the difference in the nonlinear dynamic responses predicted by different homogenization schemes decreases by increasing the power-law indices, and the variation of the material properties along the beam length in the 2D-FG beam mitigates this difference. The effects of the material gradation, the moving load velocity and the homogenization scheme on the nonlinear dynamic behaviour are studied in detail. The difference in dynamic responses obtained from linear and nonlinear dynamic analyses is also examined and discussed. [ABSTRACT FROM AUTHOR]

Curved shell structures with variable cross-sections are extensively applied in options for deep space exploration and on-orbit operation, due to their better mechanical properties compared to traditional materials. However, these structures also pose challenging dynamic modeling issues due to their nonlinear geometry and high flexibility. In this paper, the improved absolute nodal coordinate formulation (S-A-ANCF) is proposed for analyzing the dynamic behaviors of curved shells with variable cross-sections. Firstly, the neutrosphere of the curved shell is corrected to accurately describe the displacement field. Secondly, reduction factors for meshing are proposed by considering the aspect ratio criterion and shear performance criterion, which are then combined with the Enhanced Assumed Strain (EAS) method to establish the S-A-ANCF model. Finally, the correctness of the proposed method is verified through numerical analysis, and the optimized criterion for the modeling process is analyzed. According to the numerical analysis, the proposed method effectively improves modeling accuracy and efficiency. The coupling relationships between geometry, materials, boundary conditions, and stress are illustrated. The research outcomes of this paper can provide theoretical guidance for spacecraft systems with curved shells, which are of great significance and urgently need to be studied. [ABSTRACT FROM AUTHOR]

To accurately investigate the nonlinear dynamic characteristics of a flyback converter, a fractional-order state-space averaged model of a voltage mode controlled flyback converter in continuous conduction mode is established based on fractional calculus theory. And low-frequency bifurcation maps which use PI controller parameters and reference voltage as bifurcation parameters are obtained. The low-frequency oscillation phenomenon is analyzed and compared with that of an integral-order flyback converter. The results show that under certain operating conditions, the fractional-order flyback converter exhibits low-frequency oscillations as certain circuit and control parameters change. Under the same circuit conditions, there is a difference in the stable parameter region between the fractional and integral-order models of the flyback converter. The stable zone of the fractional-order flyback converter is larger than that of the integral-order one. Therefore, the circuit is more difficult to enter a low-frequency oscillation state. The stability domain of low-frequency oscillations can be accurately predicted by using the small signal model of the fractional-order flyback converter. Finally, by performing circuit simulations and hardware-in-the-loop experiments, the rationality and correctness of the theoretical analysis are verified. [ABSTRACT FROM AUTHOR]

The paper utilizes a novel approach for the dynamic design of automotive turbocharger rotors by employing nonlinear dynamics of time periodic systems, emphasizing the influence of bearing design variables to prevent sub-synchronous components in system's response. The investigation focuses on the response of an unbalanced turbocharger rotor on floating ring bearings using a collocation-type method which has been developed for the needs of the work, being then integrated with pseudo arc length continuation for the calculation of unstable solution branches of the system, in several design sets, and with poor initial values. The analytical model includes a rigid rotor model and short bearing approximations for the two floating ring bearings, which introduce strong nonlinear forces in series (inner film and outer film at each bearing). Floquet theory is employed to analyse the non-autonomous dynamic system, and stability characteristics of the response limit cycles are assessed through Floquet multipliers, whose magnitude serves as a stability index in the algorithm. A genetic algorithm based multi-objective optimization is combined to the robust collocation-type method to achieve reduced values for Floquet multipliers, ensuring that response limit cycles maintain stability and periodicity, thereby preventing the occurrence of bifurcations which normally lead to sub-synchronous response components. Twelve design variables are computed to satisfy low rotor eccentricity and power loss. Acceptable design sets are verified for efficacy by assessing system response through time integration, akin to a virtual experiment. This approach significantly reduces computational time and resource requirements compared to traditional Design of Experiment (DoE) procedures and is not constrained by complex models of the rotor, bearings, or other components. A feature of the method is that it offers an insight on the stability and its quality, rather than simply assessing a threshold speed of instability. [ABSTRACT FROM AUTHOR]

Closed differential gear transmission systems are widely used in applications such as wind turbines and aviation equipment, yet the highly complex 3D nonlinear dynamics of these systems, particularly with floating herringbone gears, have not been adequately explored. Nevertheless, there is an urgent need for a specialized analytical model for the 3D floating of herringbone gears in space, which is crucial for studying the nonlinear dynamic behavior of gear systems. This article introduces a novel 3D floating analysis method that accounts for dynamic meshing parameters, coupled dynamic backlash with multiple clearances, and Time-Varying Meshing Stiffness (TVMS) of floating gears. Building on this approach, the study develops a 134-degree-of-freedom Bending Torsion Axial Pendular (BTAP) nonlinear dynamic model for the Coaxial Reverse Closed Differential Herringbone Gear Transmission System (CRCDHGTS). The model investigates the system's bifurcation characteristics and vibration behavior under varying radial, axial, and pendular floating conditions and is validated through bench vibration experiments. This model significantly enhances the accuracy of predicting the nonlinear dynamics of multi-degree-of-freedom systems operating under multiple clearance couplings, outperforming traditional models. The findings indicate that maintaining the radial floating value of gears within 0-20 μm ensures relatively stable dynamic behavior, avoiding multi-periodic and chaotic motion. Axial floating introduces diverse bifurcation characteristics, with values exceeding 0.28 μm leading to instability. Additionally, a gear end-face deviation angle around the X and Y axes greater than 0.007° results in complex bifurcation patterns and an increased risk of chaotic motion. This work establishes a theoretical foundation for 3D floating nonlinear vibration analysis in planetary gear transmission systems. [ABSTRACT FROM AUTHOR]

In this study, a mathematical model was developed to investigate the effect of the squeeze film on the dynamic characteristics of a flexible tube in an otherwise rigid tube array subjected to cross-flow. The vibration responses of the tube system were calculated to reveal the nonlinear dynamics of the tube system with squeeze film. The tube bundle's bifurcation and post-instability characteristics were analyzed, and the instability mechanism was revealed, taking into account the effect of the squeeze film. The numerical results showed that the thickness of the squeeze film is a critical parameter affecting the instability and the dynamic response of the tube bundles system. The study found that oscillation instability occurs at the initial equilibrium position when the squeeze film thickness is large. Conversely, when the squeeze film thickness is small, static instability occurs at the initial equilibrium position, and the limited cycle motion occurs at a new equilibrium position near the boundary of the squeeze film. [ABSTRACT FROM AUTHOR]

The application of nonlinear dynamics in neuroscience has provided essential insights into the functioning of the brain, shedding light on its complex behaviors and functions. This review reflects on the remarkable developments achieved in computational neuroscience, an emerging discipline that examines how the brain operates in terms of the information-processing features that constitute the nervous system's construction. This comprehensive review covers a broad range of topics, including physiology, nonlinear dynamical methods for analyzing neural computation involving neural oscillations, synchronization events, chaotic dynamics, and network connections, brain circuit simulation, and tools for neuromorphic computation. In addition, we look at how nonlinear dynamics might help us comprehend neurological disorders, cognitive functioning, and the dynamical behavior of neural networks. [ABSTRACT FROM AUTHOR]

Qualitative changes can occur in the dynamics of nonlinear systems even for small parameter variations. Such changes are manifestations of bifurcation in dynamical systems. In the context of differential game theory, bifurcations offer insights into the underlying mechanisms driving strategic interactions and identify transitions between different types of behavior. Such critical transitions are tipping points that can dramatically change the outcomes of the game. This work explores the possibility of predicting such qualitative shifts, including supercritical Hopf bifurcations, before they occur using a data-driven forecasting technique. This concept is demonstrated for an attacker–defender game in a limited resource scenario and for an active cybersecurity defense game. The time histories of the system dynamics as it approaches a bifurcation allow one player to detect the existence of bifurcations. This capability provides that player insights into the dynamics of the game and potential defense mechanisms in resource-constrained scenarios. [ABSTRACT FROM AUTHOR]

Numerical continuation tools are nowadays standard to analyse nonlinear dynamical systems by numerical means. These powerful methods are unfortunately not available in real experiments without having access to an accurate mathematical model. Implementing such a concept in real world experiments using control and data processing to track unstable states and their bifurcations, requires robust control techniques with large basins and good global properties. Here we propose design principles for control techniques for periodic states which lead to large basins and which are robust, without the need to have access to a detailed mathematical model. Our analytic considerations for the control design will be based on weakly nonlinear analysis of periodically driven oscillator systems. We then demonstrate by numerical means that in strong nonlinear regimes successful control with large basins of attraction can be achieved when only plain time series data are available. [ABSTRACT FROM AUTHOR]

Since the inception of nonlinear vibration theory, the majority of research has been focused on the elastic beams connected to a variety of nonlinear factors. Notwithstanding this, coupling beam systems with nonlinear coupling elements have been the subject of few investigations. In light of the fact that numerous coupling beam systems are typically connected via multiple couplers, this study develops a vibration model for two beams coupled by multiple nonlinear elements exhibiting cubic stiffness. The Lagrange method is utilized to compute the magnitude responses of the beam system. Once the accuracy and consistency of the magnitude responses associated with the beam system have been confirmed, a thorough investigation is conducted into the impact of nonlinear elements on the magnitude responses of two beams joined by multiple nonlinear elements exhibiting cubic stiffness. Nonlinear responses, such as peak jumping, intricate responses, and shifting resonance regions, are determined to be the result of nonlinear elements, according to simulation results. Modulating the parameters of nonlinear elements in a rational manner facilitates the regulation of vibrations across multiple resonance regions of the beam system. Parameter changes of nonlinear elements have a substantial impact on both the vibration states and peak values of magnitude responses for single-frequency vibration excitation in resonance regions. The incorporation of nonlinear components into the coupling beam system enables the regulation of both frequency and single-frequency responses. In the case of low damping, nonlinear vibration control for a system consisting of two beams through the use of multiple nonlinear elements with cubic stiffness is more effective. [ABSTRACT FROM AUTHOR]

This paper presents a compact method for selecting the suboptimal number of clusters in unsupervised clustering, which is comparable in complexity to the well-known elbow method, silhouette score and gap statistic, but has been upgraded for clustering with the dominant overlaps. It is primarily based on heuristics and combines human reasoning with the deterministic qualitative analysis of clustering as a mapping from Euclidean space to the unstructured space of cognitive decision making and labeling. Epistemic stability as a notation involves a methodological approach that takes into account the available knowledge in the observed data set and avoids biases and effects on the objectivity of clustering. The stability discussion is also integrated into the assigned and naturally quantitative analysis of the dataset, not to regulate the clustering, but to learn from the pattern of instability. The method is applied to the specific task of classifying medical images from pre-selected image sets based on the associated metadata to determine the homogeneity of the analyzed clusters. However, it is also applicable to any other example of datasets that exhibit statistically multivariate problems with dominant overlaps. In the mathematical discussion of the method presented, the constrained conditions for datasets are established by definitions and assumptions, followed by the central mathematical propositions of the method of epistemic stability. [ABSTRACT FROM AUTHOR]

In this work, a control strategy based on fuzzy sliding mode control (FSMC) is applied to effectively manage the large-amplitude chaotic vibrations exhibited by a simply supported beam. The analysis considers the nonlinear beam structure, which is subjected to an external load. Hamilton's principle is employed, and the equations of motion are derived for the studied structure. The 3rd Galerkin discretization is employed to derive the ordinary differential governing equation of the structure. A control strategy is presented to decrease the response of the obtained multidimensional system. The vibration of a one-dimensional system is compared with that of the derived multidimensional system. As shown throughout the study, a multidimensional nonlinear system of the structure must be considered for accurate dynamic estimation. By using the recurrent neural network (RNN) model, we can accurately predict chaotic motion and effectively apply control strategies to suppress chaotic motion. The efficacy and suitability of the employed control strategy have been demonstrated by controlling chaos in the beam's multidimensional system. [ABSTRACT FROM AUTHOR]

In this paper, the dynamic behavior of one degree-of-freedom oscillator subject to stick–slip and wear phenomena at the contact interface with a rigid substrate is investigated. The motion of the oscillator, induced by a harmonic excitation, depends on the tangential contact forces, exchanged with the rigid soil, which are modeled through piecewise nonlinear constitutive laws, accounting for stick–slip phenomena due to friction as well as wear due to abrasion, already developed by the authors in a previous work. The nonlinear ordinary differential equations governing the problem are derived, whose solution is numerically obtained via a typical Runge–Kutta-based algorithm. The main target of this study is to analyze and discuss the strong nonlinear behavior, descending from the presence of stick–slip and wear phenomena, thus investigating the effect of the different interface modeling. In this framework, the analysis is carried out considering the whole evolution of non-smooth contact laws, starting from the virgin interface. [ABSTRACT FROM AUTHOR]

To achieve self-powered sensing when complex dynamics exist in fluid-conveying pipes, a novel piezoelectric energy harvesting configuration of cantilevered fluid-conveying pipes with an integrated stopper is proposed to investigate nonlinear dynamics, and elucidate the dynamic mechanism to enhance the energy harvesting performance. The nonlinear governing equation of this configuration was established by applying Hamilton's principle, and a set of ordinary differential equations was obtained using the Galerkin method. Considering the influence of a piezoelectric layer, the mode shapes with various orders of this configuration were determined by adopting the differential quadrature method. The harmonic balance method combined with the pseudo-arc length extension method was used to track the frequency responses, and the effectiveness of these responses was confirmed by comparing the analytical solutions to the numerical solutions obtained by the Runge–Kutta method. The global bifurcation diagrams, along with the phase trajectories, power spectra, and Poincaré maps, are presented to predict complex nonlinear dynamic behaviors, such as the coexistence of the system's periodic motion and chaotic motion. The results reveal that the impact force nonlinearity caused by the stopper can effectively improve the energy harvesting efficiency and make the dynamic behavior exhibit softening or hardening characteristics. Parametric investigations were conducted for the flow velocity, resistance, stiffness, and stopper position. The numerical examples reveal that the proposed system plays an important role in vibration suppression and energy harvesting. [ABSTRACT FROM AUTHOR]

This work presents a hybrid multidirectional mechanical energy harvester to enhance the performance of a cantilever-based harvester when subjected to multidirectional excitations. The multidirectional capabilities are achieved by employing a pendulum structure. Hybrid transduction is provided by combining a piezoelectric element and an electromagnetic transducer. A reduced-order model is presented based on the electromechanical Lagrangian formulation, and numerical analyses are performed to characterize the system behavior. A comparison based on energy harvesting performance is established among the novel multidirectional hybrid energy harvester (MHEH), the classical piezoelectric harvester (CPEH), and a multidirectional piezoelectric harvester (MPEH). Results show that the addition of the pendulum alone indeed provides multidirectional capabilities, but the overall performance can be reduced in some scenarios since it works as an energy absorber. This limitation is overcome by the hybridization strategy of the MHEH, by incorporating an electromagnetic transducer into the pendulum support. Overall, a significant improvement is achieved in all scenarios by utilizing the hybrid system. [ABSTRACT FROM AUTHOR]

The ultimate isolation offered by levitation provides new opportunities for studying fundamental science and realizing ultra-sensitive floating sensors. Among different levitation schemes, diamagnetic levitation is attractive because it allows stable levitation at room temperature without a continuous power supply. While the dynamics of diamagnetically levitating objects in the linear regime are well studied, their nonlinear dynamics have received little attention. Here, we experimentally and theoretically study the nonlinear dynamic response of graphite resonators that levitate in permanent magnetic traps. By large amplitude actuation, we drive the resonators into nonlinear regime and measure their motion using laser Doppler interferometry. Unlike other magnetic levitation systems, here we observe a resonance frequency reduction with amplitude in a diamagnetic levitation system that we attribute to the softening effect of the magnetic force. We then analyze the asymmetric magnetic potential and construct a model that captures the experimental nonlinear dynamic behavior over a wide range of excitation forces. We also investigate the linearity of the damping forces on the levitating resonator, and show that although eddy current damping remains linear over a large range, gas damping opens a route for tuning nonlinear damping forces via the squeeze-film effect. [ABSTRACT FROM AUTHOR]

Large amplitude vibration of transmission line seriously affects the structural safety. Due to the low bending stiffness of superhigh transmission tower, vortex-induced excitation combining with support motion induced by the tower will cause significant complex dynamic behaviors of the transmission line. To reveal dynamic behaviors, this paper newly proposes a suspended cable model of the transmission line subjected to the boundary motion and vortex-induced vibration. Dynamic mechanism and vibration energy transfer are focused in the condition of primary and subharmonic resonances. Innovative behaviors of the transmission line under two excitations are revealed. Firstly, vortex-induced excitation is very weak and support motion usually plays a dominate role in the dynamic responses. Large amplitude vibration of transmission line observed in practice should be caused more by tower tip motion and the vortex-induced vibration is the incentive. Secondly, different weak support motion can cause different effect on dynamic responses of transmission line under vortex-induced vibration reflecting by different lock-in phenomenon, which leads us the application of active control measure in engineering. [ABSTRACT FROM AUTHOR]

The multi-gear parallel drive system of TBM is susceptible to many nonlinear factors in the driving process, which seriously affects the dynamic performance of the system. This paper takes the six-gear parallel transmission system as the research object, introduces the influence of several nonlinear factors such as thermal deformation, establishes the dynamic model of the system, adopts the Runge-Kutta method to carry out simulation calculation, and studies the dynamic characteristics of the system by combining the bifurcation diagram and Lyapunov diagram. The results indicate that when the temperature is below 58.43 °C or above 70.4 °C, with a stiffness coefficient below 0.35 and a damping ratio above 0.069, it can suppress chaotic motion, reduce system vibration and noise. Furthermore, beyond 58.43 °C and 70.4 °C, variations in stiffness and damping ratios have a minimal impact on the system's motion characteristics, indicating that higher temperatures can enhance system stability. [ABSTRACT FROM AUTHOR]

Based on empirical evidences and previous studies, we introduce and mathematically study a perception-driven model for the dynamics of buyer populations in markets of perishable goods. Buyer behaviours are driven partly by some loyalty to the sellers that they previously purchased at, and partly by the sensitivity to the intrinsic attractiveness of each seller in the market. On the other hand, the sellers update they attractiveness in time according to the difference between the volume of their clientele and the mean volume of buyers in the market, optimising either their profit when this difference is favourable or their competitiveness otherwise. While this negative feedback mechanism is a source of instability that promotes oscillatory behaviour, our analysis identifies the critical features of the dynamics that are responsible for the asymptotic stability of the stationary states, both in their immediate neighbourhood and globally in phase space. Altogether, this study provides mathematical insights into the consequences of introducing feedback into buyer–seller interactions in such markets, with emphasis on identifying conditions for long-term constancy of clientele volumes. [ABSTRACT FROM AUTHOR]

We present a novel data-driven Model Predictive Control (MPC) algorithm for nonlinear systems. The method is based on recent extensions of behavioural theory and Willem's Fundamental Lemma for nonlinear systems by the means of adequate Input–Output (IO) quasi-Linear Parameter-Varying (qLPV) embeddings. Thus, the MPC is formulated to ensure regulation and IO constraints satisfaction, based only on measured datasets of sufficient length (and under persistent excitation). The main innovation is to consider the knowledge of the function that maps the qLPV realisation, and apply an extrapolation procedure in order to generate the corresponding future scheduling trajectories, at each sample. Accordingly, we briefly discuss the issues of closed-loop IO stability and recursive feasibility certificates of the method. The algorithm is tested and discussed with the aid of a numerical application. [ABSTRACT FROM AUTHOR]

The wear of rotating pair is a significant factor for the failure of mechanical systems. Currently, some scholars have undertaken investigations on wear clearance, but these works often concentrate on basic systems with even wear clearance, while investigations on multibody systems with uneven wear clearances remains scarce. In addition, the research on wear clearance often focuses on theoretical exploration and computer simulation, while the test research is relatively few. Therefore, a modeling method for 9-bar mechanism with multiple uneven wear clearances is derived by using the Archard model and Lagrange method, the effects of wear times and initial clearance values on dynamic characteristics and nonlinear dynamics of mechanism considering uneven wear clearances are investigated. The test bed of 9-bar mechanism considering clearances is designed and the validity of the theoretical model has been confirmed through a comparison between the collected test data and theoretical data. This paper supplies theory for accurately predicting the dynamic characteristics of multibody system containing uneven wear clearances, and provides proof for identifying and repairing the design defects of mechanism. [ABSTRACT FROM AUTHOR]

Gear cracks may occur during the operation of planetary driveline, leading to a huge safety hazard. However, few studies have been conducted to investigate the influence mechanism of planetary driveline vibration with crack extension. In order to simulate the actual working conditions, a damage dynamics model of the planetary gear train is constructed. Firstly, the system dynamics differential equations are established based on the dynamics model and solved to obtain the bifurcation diagram, time-domain diagram, phase diagram, three-dimensional wavelet diagram, three-dimensional spectrogram, and meshing force diagram of the system to investigate the effects of the excitation frequency and the degree of cracking of the gears on the vibration characteristics of the system. Then, the global bifurcation diagram of the system is constructed by using the cell mapping method, and the evolution mechanism of the global vibration characteristics of the system is explored according to the coexisting states of the system. In addition, the proposed dynamics model is verified by planetary gear train failure simulation experiments. The results show that the system has similar global characteristics under healthy operating conditions and cracked faults, and the system instability increases with the gear crack extension. Therefore, it is valuable to predict the planetary gear life by analysing the global vibration characteristics of the system. [ABSTRACT FROM AUTHOR]

Objective: In this work we intend to design a system to classify human arousal at five levels (i.e., five stress levels) using four peripheral bio signals including photo-plethysmography measurements (PPG), galvanic skin response (GSR), thorax respiration (TR) and abdominal respiration (AR). Method: A total of 98 young people voluntarily participated in this study, including 65 men and 33 women with an average age of 24.48 ± 4.26 years. We induced five levels of mental stress in subjects through the Stroop test. A range of physiological features from different analysis domains, including statistical, frequency, and geometrical analyzes, as well as recurrence quantification analysis (RQA) and detrended fluctuation analysis (DFA) were extracted to find out the best arousal-related features and to correlate them with arousal states. Classification of the five arousal levels is performed by a simple naïve Bayes classifier. Results: Accuracies of 58.45%, 57.1% and 69.13% were obtained using linear features, nonlinear features and a combination of them, respectively. The combination of linear and nonlinear features resulted in the largest average accuracy of 69.13%, ICC of 88.12% and F1 of 69.43% values in the classification of five levels of mental stress. Conclusion: This paper suggested that combining linear and nonlinear dynamic methods for the analysis of physiological data could help improve the accuracy of the recognition of arousal levels. However, it should be noted that combining multiple modalities (here, PPG, GSR and respiration modalities) by equally weighting them may not always be a good approach to improve accuracy. [ABSTRACT FROM AUTHOR]

During the trajectory tracking of robotic manipulators, many factors including dead zones, saturation, and uncertain dynamics, greatly increase the modeling and control difficulty. Aiming for this issue, a nonlinear active disturbance rejection control (NADRC)-based control strategy is proposed for robotic manipulators. In this controller, an extended state observer is introduced on basis of the dynamic model, to observe the extend state of model uncertainties and external disturbances. Then, in combination with the nonlinear feedback control structure, the robust trajectory tracking of robotic manipulators is achieved. Furthermore, to optimize the key parameters of the controller, an improved particle swarm optimization algorithm (IPSO) is designed using chaos theory, which improves the tracking accuracy of the proposed NDRC strategy effectively. Finally, using comparative studies, the effectiveness of the proposed control strategy is demonstrated by comparing with several commonly used controllers. [ABSTRACT FROM AUTHOR]

In the space microgravity environment, joint clearance is an important factor affecting the motion accuracy and stability of the mechanical system. This paper analyzes the dynamics of the four-bar mechanism with clearance in the microgravity environment. The two-state model is employed to describe the revolute joint with clearance. The continuous contact force model and the improved Coulomb friction model are selected to calculate the normal collision force and tangential friction force under the contact state, respectively. On this basis, the dynamic equation of the multibody system is derived, which is verified by both the analog experiments on the ground and simulations. Furthermore, parametric analysis and nonlinear characterization are presented. The results show that the existence of clearance will cause collision impact at the kinematic pair, which reduces the kinematic accuracy and operational stability of the mechanism. The joint clearance destroys the periodicity of the mechanism motion and increases the chaos phenomenon of the system. It could be concluded that properly reducing the clearance size, reducing the rotational speed, and increasing the friction coefficient can reduce the collision impact between the moving components. [ABSTRACT FROM AUTHOR]

To reduce breast motion with a bra, we need to understand what drives the motion of the breasts, and what variables change as support increases. Quantifying breast-torso coordination and movement complexity across the gait cycle may offer deeper insights than previously reported discrete time lag. We aimed to compare breast-torso coordination and mutual influence across breast support conditions during running. Twelve female participants ran on a treadmill at 10 km h−1 with an encapsulation and compression sports bra, and in no bra. Nipple and torso position was recorded. Vector coding, granger causality and transfer entropy were calculated within gait cycles. In both bra conditions, a greater percentage of gait cycles was spent with the breast and torso in-phase (> 90%) compared to no bra running (~ 66%, p < 0.001), with most time spent in-phase in the encapsulation versus compression bra (p = 0.006). There was a main effect of breast support condition on Granger causality (p < 0.001), both from breast to torso and torso to breast. Transfer of information was highest from torso to breast, compared to breast to torso in all conditions. Overall, these results provide novel insight into the mutual and complex interaction between the breast and the torso while running in different bra conditions. The approaches presented allow for a greater understanding of bra support conditions than existing discrete measures, which may relate to comfort and performance. Therefore, measures of coupling, predictability and transfer of complexity should be employed in future work examining these features. [ABSTRACT FROM AUTHOR]

The celebrated Hirota equation has important applications in nonlinear optics and quantum physics. This paper proposes a new type of time-varying spectral Hirota (tvsH) equation with variable coefficients and constructs its soliton solutions by extending the Riemann–Hilbert (RH) method. Specifically, Lax representation of the tvsH equation is first provided, which consists of time-varying spectral matrices, and the corresponding RH problem is further established by analyzing the Lax pair. Then, by combining inverse scattering and the spatiotemporal evolution of matrix vector solutions, an explicit expression for n-soliton solution of the tvsH equation is constructed in the absence of reflection potential. In addition, the collision soliton dynamics of the tvsH equation under isospectral and non-isospectral conditions are analyzed by modulating the time-varying coefficients. Most importantly, through the dynamic analysis of single and double solitons in the tvsH equation, we discover some new waveforms that have never been reported before, such as oscillating parabolic solitons and amplitude parabolic variation solitons. These waveforms may have significant theoretical and practical implications. [ABSTRACT FROM AUTHOR]

A novel model based on optically pumped spin-polarized vertical-cavity surface-emitting laser (spin-VCSELs) with negative optoelectronic feedback (NOEF) is implemented and analyzed in this paper. The bifurcation analysis is used to systematically study the influence of key parameters on the output dynamic behavior of the proposed model. In addition, plentiful dynamical regimes are generated in a variety of mapping diagrams, which visually show several different color regions. The direct numerical simulations in detail explain the evolution process of the system from steady state, periodic state, period-doubling state, and quasi-periodic state to chaotic state, and reveal the dependence of the rich dynamic behaviors of the model on the NOEF parameters. We find that the enhancement of feedback intensity and feedback delay time can make the system easier to enter the complex dynamic regions. At the same time, the C 0 complexity algorithm is used to estimate the complexity of the proposed model. The results show that the introduction of NOEF has a significant effect on the complexity enhancement. Furthermore, the positive effects of pumping intensity, pump ellipticity and linewidth enhancement factor on the dynamic behavior evolution of the model are also evident in the mapping diagrams. Conversely, the spin-flip relaxation rate can suppress complex dynamic behavior. By studying the dynamic behavior of external and internal parameters, it provides a theoretical basis for adjusting the dynamic mechanism and to explore the extended model of spin-VCSELs based on NOEF. [ABSTRACT FROM AUTHOR]

The Gross–Pitaevskii equation is solved by analytic methods for an external double-well potential, that is, an infinite square well plus a δ -function central barrier. We find solutions that have the symmetry of the non-interacting Hamiltonian as well as asymmetric solutions that bifurcate from the symmetric solutions for attractive interactions and from the antisymmetric solutions for repulsive interactions. We present a variational approximation to the asymmetric state as well as an approximate numerical approach. We compare with other approximate methods. Stability of the states is considered. [ABSTRACT FROM AUTHOR]

The Gross–Pitaevskii equation (GPE) in a double-well potential produces solutions that break the symmetry of the underlying non-interacting Hamiltonian, i.e., asymmetric solutions. The GPE is derived from the more general second-quantized Fock Schr o ¨ dinger equation (FSE). We investigate whether such solutions appear in the more general case or are artifacts of the GPE. We use two-mode analyses for a variational treatment of the GPE and to treat the Fock equation. An exact diagonalization of the FSE in dual condensates yields degenerate ground states that are very accurately fitted by phase-state representations of the degenerate asymmetric states found in the GPE. The superposition of degenerate asymmetrical states forms a cat state. An alternative form of cat state results from a change of the two-mode basis set. [ABSTRACT FROM AUTHOR]

Tall wind turbines are structures susceptible to high vibration levels, which may affect their optimal functioning and, ultimately, their overall structural stability. One alternative to minimize undesirable vibrations is to install vibration control devices. Various such devices are documented in the literature, with one noteworthy example being the tuned liquid column damper (TLCD), which is a vertical column filled with a liquid mounted at the top of the structure. When the main structure is dynamically excited, the appropriate TLCD vibrates out of phase with the structure, controlling its dynamic response. In this work, the nonlinear vibrations and control of a wind tower-nacelle-blade system subjected to an external harmonic force are studied. Nonlinear Euler–Bernoulli beam theory, together with the Rayleigh–Ritz method and Hamilton's principle, are used to obtain a set of nonlinear equations of motion, which are, in turn, solved by the Runge–Kutta method. A TLCD device located at the top of the tower is used to control vibrations. First, the effect of blade rotation on the natural frequencies of the system is studied. Second, resonance curves are obtained to study the effect of blade rotation and the frequency of the external force on the nonlinear vibrations of the tower, and the effect of the TLCD on vibration control is also analyzed. This study provides valuable perspectives on the dynamics of offshore wind turbines, contributing to the development of wind energy systems that are more robust and adaptable. [ABSTRACT FROM AUTHOR]

Chronic Myeloid Leukemia is a blood cancer for which standard therapy with Tyrosine-Kinase Inhibitors is successful in the majority of patients. After discontinuation of treatment half of the well-responding patients either present undetectable levels of tumor cells for a long time or exhibit sustained fluctuations of tumor load oscillating at very low levels. Motivated by the consequent question of whether the observed kinetics reflect periodic oscillations emerging from tumor-immune interactions, in this work, we analyze a system of ordinary differential equations describing the immune response to CML where both the functional response against leukemia and the immune recruitment exhibit optimal activation windows. Besides investigating the stability of the equilibrium points, we provide rigorous proofs that the model exhibits at least two types of bifurcations: a transcritical bifurcation around the tumor-free equilibrium point and a Hopf bifurcation around a biologically plausible equilibrium point, providing an affirmative answer to our initial question. Focusing our attention on the Hopf bifurcation, we examine the emergence of limit cycles and analyze their stability through the calculation of Lyapunov coefficients. Then we illustrate our theoretical results with numerical simulations based on clinically relevant parameters. Besides the mathematical interest, our results suggest that the fluctuating levels of low tumor load observed in CML patients may be a consequence of periodic orbits arising from predator–prey-like interactions. [ABSTRACT FROM AUTHOR]

To analyze the vibration characteristics of the electromechanical coupling transmission system of electrical vehicles under gear faults, an electromechanical coupling transmission system including two-stage meshing gear and motor system is established. Combining the effects of backlash, transmission error, and time-varying mesh stiffness on the system, the dynamic model of the transmission system includes electromechanical coupling for electrical vehicles is established by using torque as a link between mechanical and electrical systems. The meshing stiffness calculation of different fault extent is introduced to explore the nonlinear vibration characteristics of the transmission system under various faults. The vibration characteristics of systems are analyzed under different rotational speeds, impact loads, and FTP (Federal Test Procedure) actual road conditions. The results show that the cracked gear generates periodic pulses, and its vibration amplitude increases with the extent of crack. Under the same crack extent, the vibration amplitude decreases with the increase of rotational speed and impact load. At the same time, the current receives the same periodic pulse. [ABSTRACT FROM AUTHOR]