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In order to enhance the performance of Transformer models for long-term multivariate forecasting while minimizing computational demands, this paper introduces the Joint Time-Frequency Domain Transformer (JTFT). JTFT combines time and frequency domain representations to make predictions. The frequency domain representation efficiently extracts multi-scale dependencies while maintaining sparsity by utilizing a small number of learnable frequencies. Simultaneously, the time domain (TD) representation is derived from a fixed number of the most recent data points, strengthening the modeling of local relationships and mitigating the effects of non-stationarity. Importantly, the length of the representation remains independent of the input sequence length, enabling JTFT to achieve linear computational complexity. Furthermore, a low-rank attention layer is proposed to efficiently capture cross-dimensional dependencies, thus preventing performance degradation resulting from the entanglement of temporal and channel-wise modeling. Experimental results on eight real-world datasets demonstrate that JTFT outperforms state-of-the-art baselines in predictive performance. [ABSTRACT FROM AUTHOR]

Fault diagnosis of rotating machinery is crucial to improve safety, enhance reliability and reduce maintenance cost. The manual feature extraction and selection of traditional fault diagnosis methods depend on signal processing skills and expert experience, which is labor-intensive and time-consuming. As a typical intelligent fault diagnosis method, the convolutional neural network automatically learns features from original data, but it is extremely difficult to design and train a deep network architecture. This paper proposes a fault diagnosis scheme combined of hierarchical symbolic analysis (HSA) and convolutional neural network (CNN), which achieves laborsaving and timesaving preliminary feature extraction and accomplishes automatically feature learning with simplified network architecture. Firstly, hierarchical symbolic analysis is employed to extract features from original signals. The extracted features are able to identify different health conditions under various operating conditions. Then, convolutional neural network instead of human labor is used to learn the complex non-linear relationship between features and health conditions automatically. The architecture of CNN diagnosis model is simple and convenient to implement. Finally, a centrifugal pump dataset and a motor bearing dataset are adopted to validate the effectiveness of the proposed method. The diagnosis results show that the proposed method exhibits superior performance compared with shallow methods and deep learning methods. • HSA-CNN is proposed for fault diagnosis of rotating machinery. • Hierarchical symbolic analysis is proposed to extract features. • The method performs superior diagnosis capacity with a simple network architecture. • Two case studies show the effectiveness and superiority of HSA-CNN. [ABSTRACT FROM AUTHOR]

The singularity theory is applied to study the bifurcation behaviors of a reduced rotor model obtained by nonlinear transient POD method in this paper. A six degrees of freedom (DOFs) rotor model with cubically nonlinear stiffness supporting at both ends is established by the Newton's second law. The nonlinear transient POD method is used to reduce a six-DOFs model to a one-DOF one. The reduced model reserves the dynamical characteristics and occupies most POM energy of the original one. The singularity of the reduced system is analyzed, which replaces the original system. The bifurcation equation of the reduced model indicates that it is a high co-dimension bifurcation problem with co-dimension 6, and the universal unfolding (UN) is provided. The transient sets of six unfolding parameters, the bifurcation diagrams between the bifurcation parameter and the state variable are plotted. The results obtained in this paper present a new kind of method to study the UN theory of multi-DOFs rotor system. [ABSTRACT FROM AUTHOR]

The quality of models built by machine learning algorithms mostly depends on the careful tuning of hyper-parameters and feature weights. This paper introduces a novel scheme to optimize hyper-parameters and features by using the Ensemble Kalman Filter (EnKF), which is an iterative optimization algorithm used for high-dimensional nonlinear systems. We build a framework for applying the EnKF method on parameter optimization problems. We propose ensemble evolution to converge to the global optimum. We also optimize the EnKF calculation for large datasets by using the computationally efficient UR decomposition. To demonstrate the performance of our proposed design, we apply our approach for the tuning problem of Support Vector Machines. Experimental results show that the better global optima can be identified by our approach with acceptable computation cost compared to three state-of-the-art Bayesian optimization methods (SMAC, TPE and SPEARMINT). [ABSTRACT FROM AUTHOR]

This paper focuses on the nonlinear responses of a cracked rotor-ball bearing system caused by aircraft flight maneuvers. The equations of motion of the system are formulated with the consideration of the breathing mechanism of a transverse crack and the maneuver load of a climbing-diving flight. The fourth order Runge-Kutta method is employed to detect the nonlinear responses of the system, which are reflected by bifurcation diagrams, power spectrums, maximum Lyapunov exponent, phase portraits and Poincaré sections. It is shown that the super-harmonic responses of the system are affected significantly by the maneuver load under sub-critical speeds. Plenty of quasi-periodic motions are obtained, and a variety of complex nonlinear behaviors including bifurcations and jumping phenomenon are observed near 1/4, 1/3, 2/5 and 1/2 critical speeds when the maneuver load increases from 0 to 10 g. The nonlinear responses of the system influenced by crack stiffness, bearing clearance and rotor eccentricity are also investigated. Chaotic motions are demonstrated when the crack stiffness or the bearing clearance increases across a critical value. However, the responses maintain quasi-periodic when the rotor eccentricity changes. The results will contribute to a better understanding of the nonlinear dynamic behaviors of cracked rotors in flight maneuvers. [ABSTRACT FROM AUTHOR]

The time-space domain finite difference methods reduce numerical dispersion effectively by minimizing the error in the joint time–space domain. However, their interpolating coefficients are related with the Courant numbers, leading to significantly extra time costs for loading the coefficients consecutively according to velocity in heterogeneous models. In the present study, we develop a time-space domain stereo finite difference (TSSFD) method for 3D scalar wave equation. The method propagates both the displacements and their gradients simultaneously to keep more information of the wavefields, and minimizes the maximum phase velocity error directly using constant interpolation coefficients for different Courant numbers. We obtain the optimal constant coefficients by combining the truncated Taylor series approximation and the time-space domain optimization, and adjust the coefficients to improve the stability condition. Subsequent investigation shows that the TSSFD can suppress numerical dispersion effectively with high computational efficiency. The maximum phase velocity error of the TSSFD is just 3.09% even with only 2 sampling points per minimum wavelength when the Courant number is 0.4. Numerical experiments show that to generate wavefields with no visible numerical dispersion, the computational efficiency of the TSSFD is 576.9%, 193.5%, 699.0%, and 191.6% of those of the 4th-order and 8th-order Lax-Wendroff correction (LWC) method, the 4th-order staggered grid method (SG), and the 8th-order optimal finite difference method (OFD), respectively. Meanwhile, the TSSFD is compatible to the unsplit convolutional perfectly matched layer (CPML) boundary condition for absorbing artificial boundaries. The efficiency and capability to handle complex velocity models make it an attractive tool in imaging methods such as acoustic reverse time migration (RTM). [ABSTRACT FROM AUTHOR]

This paper focuses on the nonlinear dynamic and bifurcation characteristics of an aircraft rotor system affected by the maneuvering flight of the aircraft. The equations of motion of the system are formulated with the consideration of the nonlinear supports of Duffing type and the sine maneuver load of a proposed maneuvering flight model. By utilizing the multiple scales method to solve the motion equations analytically, the bifurcation equations are obtained. Accordingly, the response and the bifurcation characteristics of the system are analyzed respectively. Basically, the increase of the maneuver load may increase the formant frequency as well as the primary resonance frequencies. Through numerical simulations, four different types of response characteristics of the system during the maneuvering flight are found, which are compared with the theoretical results, and it shows good qualitative agreements between them. Furthermore, the maneuver load can make an apparent effect on the bifurcation. The results in this paper will provide a better understanding for the effect of aircraft maneuvering flight on the dynamics and bifurcations of the rotor system. [ABSTRACT FROM AUTHOR]

This study focuses on the nonlinear dynamic characteristics of a single-machine infinite-bus (SMIB) power system under a periodic load disturbance. The qualitative behavior of this system is described by the well-known “swing equation”, which is a nonlinear second-order differential equation. Compared with the existing results, the generator damping in this paper, which is more close to the practical engineering, is related to the state variables of this system. In addition, Melnikov’s method is applied to obtain the threshold for the onset of chaos. The efficiency of the criteria for chaotic motion is verified via numerical simulations. Comparisons between the theoretical analysis and numerical simulation show good agreements. The results in this paper will contribute a better understanding of the nonlinear dynamic behaviors of the SMIB power system. [ABSTRACT FROM AUTHOR]

In this paper, the flutter of a compressor blade is investigated to explore the fracture failure mechanism of the blade with an assembled clearance, cubic structural nonlinearity and aerodynamic forces. Firstly, the stability of the linearized system is studied in the neighborhood of an equilibrium point and the threshold speed of the linear flutter of the blade is obtained. Then the response equations of limit cycle oscillations (LCOs) are deduced by using the averaging method, and the stability of LCOs is analyzed based on the first-order approximate theory. Comparisons with the results from the fourth-order Runge–Kutta scheme are carried out, and the accuracy of the first-order approximation of the averaging method is discussed. Finally, the influence of clearance parameter, bending stiffness and torsional rigidity on the flutter characteristics of the blade is analyzed. [ABSTRACT FROM AUTHOR]

This paper focuses on the bifurcation behaviors of a rigid rotor-squeeze film damper system considering the effect of fluid inertia. The equations of motion of the system are formulated considering π oil film model with fluid inertia. Then the averaging method is employed to obtain the bifurcation equation of the system model. By using the C-L method, three different modes of bifurcation behaviors are found from the three regions divided by the transition sets, namely bifurcation set and hysteresis set in system parameter plane. By changing the value of Reynolds number that reflects the fluid inertia of the squeeze film damper, the hysteresis set is moved obviously; it is shown that the fluid inertia plays an important role in determining the bifurcation behaviors of the system. Meanwhile, the bifurcation behaviors of system are affected significantly by the fluid inertia when the bearing coefficient locates within a certain region. Thus in this situation, the fluid inertia must be taken into account for theoretical analysis. Direct numerical simulation is also carried out by using the 4th order Runge-Kutta method to verify the theoretical results. The results obtained in this paper will provide a fundamental theory for designing an effective squeeze film damper. [ABSTRACT FROM AUTHOR]

• The nonlinear dynamics and thermal bidirectional coupling model of a rotor-ball bearing system is constructed. • The coupling characteristics of the interaction between vibration response and temperature variation are obtained. • The complicated jump phenomena and motion patterns in vibration response and temperature variation are demonstrated. • The characteristics affected by initial radial clearance, rotor eccentricity and lubricant viscosity are discussed. This paper focuses on the nonlinear dynamics and thermal bidirectional coupling characteristics of a rotor-ball bearing system. The motion equations of the rotor system are formulated by the Lagrange method, where the radial clearance of the ball bearing affected by thermal characteristics is considered. The heat transfer model of the ball bearing is established by combining the lumped parameter with the full thermal network, in which the frictional heat generation induced by the dynamic load of the ball bearing is considered. The heat transfer model is coupled with the motion equations of the rotor system via the mechanical model of the ball bearing. The dynamics and thermal bidirectional coupling model is solved by the step-by-step iterative solving procedure to detect the interaction between the vibration response of the rotor and the temperature variation of the ball bearing. The results show that the thermal expansion of the ball bearing results in the dynamical variation of the effective radial clearance, which makes a significant influence on nonlinear dynamics and thermal characteristics of the rotor-ball bearing system. On the other hand, the nonlinear dynamic response of the rotor leads to the nonlinear thermal characteristics of the ball bearing through the influence of the dynamic load. It is observed that there are more complicated jump phenomena and motion patterns in the vibration response and temperature variation compared to the case without thermal effects. Moreover, the jump phenomena affected by the initial radial clearance, rotor eccentricity, and lubricant viscosity are analyzed in detail. The results obtained in this paper can provide more insight into the bidirectional coupling mechanism of the nonlinear dynamics and thermal characteristics. [ABSTRACT FROM AUTHOR]

Abstract: The purpose of this work is to determine the solubility of greenhouse gases in different ionic liquids (ILs). Experimental values for the solubility of carbon dioxide, methane and nitrous oxide in ionic liquids are measured at different temperatures and at pressures close to atmospheric. Carbon dioxide is the most soluble gas studied with mole fraction solubility of the order of 10−2. Nitrous oxide is one order of magnitude less soluble than carbon dioxide, whereas methane is the least soluble gas. Finally, a group contribution method aimed at estimating the Henry's law constant of CO2 in ILs as a function of temperature was developed. Such a method makes it possible to predict the solubility of CO2 in ionic liquids when experimental data are unavailable. [Copyright &y& Elsevier]

Abstract: This work is focused on the possible capture of carbon dioxide using ionic liquids (ILs). Such solvents are gaining special attention since the efficiency of many processes can be enhanced by the judicious manipulation of their properties. In this work, the potential use of two ILs: 1-butyl-3-methylimidazolium diethylene-glycolmonomethylethersulfate [BMIM][MDEGSO4] and trihexyl(tetradecyl)phosphonium dodecyl-benzenesulfonate [THTDP][C12H25PhSO3] is evaluated through the measurement of the liquid–vapor equilibrium in mixture with CO2 at temperatures up to 373K and pressures up to 300bar. Experimental data indicate that 95g of CO2 can be absorbed per kg of ionic liquid. For each IL, the parameters of the PC-SAFT EoS were estimated using experimental density data measured under atmospheric pressure in a wide range of temperatures. After fitting a binary interaction parameter k ij on experimental liquid–vapor equilibria data, the model was able to describe accurately carbon dioxide solubility in these two ionic liquids. [Copyright &y& Elsevier]

Abstract: Using a combination of analytical and numerical methods, the paper studies chaotic motions of a two-dimensional airfoil with cubic nonlinearity in supersonic flow. By using the undetermined coefficient method, the homoclinic orbit is found, and the uniform convergence of the homoclinic orbit series expansion is proved. It analytically demonstrates that there exists a homoclinic orbit joining the initial equilibrium point to itself, therefore Smale horseshoe chaos occurs for this system via Siʼlnikov criterion. The system evolves into chaotic motion through period-doubling bifurcation, and is periodic again as the dimensionless airflow speed increases. While the system is periodic and chaotic alternately as the wing mass static moment about the elastic axis increases. When the nonlinear stiffness coefficient crosses its critical value, the system is always chaotic. Numerical simulations are also given, which confirm the analytical results. [Copyright &y& Elsevier]

Abstract: This study focuses on the dynamic and vibration characteristics of a four-degree of freedom gear system with local defects to explore the failure mechanism. The dynamic models of the gear system with tooth crack and spalling failure are respectively established to investigate the effect of the failures on mesh stiffness and dynamic response by numerical simulation. The differences and comparisons between the vibration signals with the tooth crack and spalling failure are discussed by using time history, phase contrail, Poincaré section, spectrum analysis and fractal dimension, which shows the different dynamic characteristics between the tooth crack and spalling failure. An experimental gearbox with tooth crack and spalling failure was designed and experiments was carried out to determine the dynamic characteristics of the faulty vibration signals. The results obtained herein show good agreement qualitatively with the theoretical analysis, which provides a theoretical basis for the fault diagnosis of gearboxes. [Copyright &y& Elsevier]

Abstract: The global bifurcations and chaotic motions are investigated analytically for an arch structure with parametric and forced excitation. The critical curves separating the chaotic and non-chaotic regions are drawn, which show that the system in the case of 1:1 resonance is more easily chaotically excited than the case of 1:2 resonance. There exist “uncontrollable regions” or “chaotic bands” for the system as the natural frequency varies. There also exists a “controllable frequency” for the system with linear and cubic parametric excitation. The system can be chaotically excited through infinite subharmonic bifurcations of odd/even orders. Numerical results agree with the analytical ones. [Copyright &y& Elsevier]

Abstract: The stability and chaotic motions of a damped satellite partially filled with liquid which is subjected to external disturbance are investigated in this paper. With linearization analysis, the stability of the two non-trivial equilibrium points is studied. The homoclinic and heteroclinic orbits are found by using the undetermined coefficient method, and the convergence of the series expansions of these two types of orbits is proved. It analytically demonstrates that there exist homoclinic orbits of the Si’lnikov type that join the two non-trivial equilibrium points to themselves, and therefore smale horseshoes and the horseshoe chaos occur for this system via the Si’lnikov criterion. In addition, there also exists a heteroclinic orbit connecting the two non-trivial equilibrium points. Numerical simulations are also given, which verify the analytical results. The system can be chaotic through period-doubling bifurcations as the amplitude of the external disturbance varies, and backward period-doubling bifurcations as the angular momentum of the rotor varies. [Copyright &y& Elsevier]

Human geranylgeranyl pyrophosphate synthase (GGPS) is an enzyme that catalyzes the synthesis of geranylgeranyl pyrophosphate (GGPP) from farnesyldiphosphate and isopentenyldiphosphate. Recombinant human GGPS was crystallized by the hanging-drop vapor diffusion method. Crystals were grown at 18°C using PEG 4000 as precipitant. Diffraction data were obtained to a resolution of 2.8 Å from a single frozen crystal belonging to space group P1, with unit-cell parameters: a = 68.9 Å, b = 107. 7 Å, c = 137. 4 Å, α = 99.6°, β = 97.6°, γ = 97.8°. [ABSTRACT FROM AUTHOR]

The method of multiple scales is applied for constructing nonlinear normal modes (NNMs) of a three-degree-of-freedom system which is discretized from a two-link flexible arm connected by a nonlinear torsional spring. The discrete system is with cubic nonlinearity and 1:3 internal resonance between the second and the third modes. The approximate solution for the NNM associated with internal resonance are presented. The NNMs determined here tend to the linear modes as the nonlinearity vanishes, which is significant for one to construct NNM. Greatly different from results of those nonlinear systems without internal resonance, it is found that the NNM involved in internal resonance include coupled and uncoupled two kinds. The bifurcation analysis of the coupled NNM of the system considered is given by means of the singularity theory. The pitchfork and hysteresis bifurcation are simultaneously found. Therefore, the number of NNM arising from the internal resonance may exceed the number of linear modes, in contrast with the case of no internal resonance, where they are equal. Curves displaying variation of the coupling extent of the coupled NNM with the internal-resonance-deturing parameter are proposed for six cases. [Copyright &y& Elsevier]

Abstract In this research note, two order reduction methods in the high-dimensional rotor systems are presented: one is the transient proper orthogonal decomposition (T-POD) method and the other is the structure order reduction (SOR) method. The accuracy of the SOR method is verified in comparison to the critical speed error, and the efficacy of the T-POD method is verified via comparing with the nonlinear instability behaviours of the original and reduced models. The SOR method is applied to compare with the T-POD method, and further verifies the efficacy of the T-POD method. The numerical results indicate that both the T-POD method and the SOR method can be applied for order reduction in the high-dimensional rotor system. [ABSTRACT FROM AUTHOR]

The national and regional carbon neutrality ambition necessitates clean power transition but also requires significant amount of generation, transmission, and storage infrastructure for renewables. Understanding the consequent material implications and embodied emissions of such energy infrastructure development with a system perspective at various geographical scales is thus important for maximizing emissions reduction and minimizing trade-offs among climate, resource, and waste targets. Previous research along this line, however, often focuses on individual subsystems (e.g. , power generation) or individual technologies (e.g. , wind energy) on a global or national scale. Here, we combined a dynamic material flow analysis model, life cycle assessment database, and scenario analysis to characterize stocks, flows, and embodied emissions of six bulk materials and thirteen critical materials associated with clean power transition from 1978 to 2050 in Guangdong province, China. We show that Guangdong's clean power transition leads to a total material stock increase from 2.9 Mt in 1980 to 45.6 Mt in 2018 and further to 95.7 Mt in 2050 under the basic renewable energy scenario (BES). The material stock in both generation and storage subsystems will grow over time, whereas that in the transmission subsystem will peak at approximately 2040 and then gradually decline. The massive expansion of wind and nuclear energy will result in a drastic rise in materials use, especially for cement and steel. A higher proportion of renewables increases energy infrastructure embodied emissions but reduces overall emissions. Future mitigation efforts and policy should not only address operational emissions through energy structure adjustment, but also curb the embodied emissions through infrastructure lifetime extension, material efficiency improvement, and material production decarbonization. [Display omitted] • We quantified material stocks, flows, and embodied emissions in power transition. • Expanding wind and nuclear power spurs heavy cement and steel use. • Material stock in transmission subsystem will peaks by 2040 and then slowly fall. • Renewables penetration increases embodied emissions but reduces overall emissions. • Extending energy infrastructure lifetime will reduce emissions. [ABSTRACT FROM AUTHOR]

• A general and efficient harmonic balance method for nonlinear dynamic simulation is proposed. • By employing the FFT technique, the Jacobian matrix is obtained in a general and efficient manner. • The constant tensor matrices devoid of reliance on the equation's specific formulation facilitates obtaining the Jacobian matrix in a general manner. • Loop computations are no longer requisite facilitates obtaining the Jacobian matrix in an efficient manner. • Computational findings across two distinct scenarios unequivocally demonstrate the superior computational efficiency of the GE-HB method. This paper presents a general and efficient harmonic balance (GE-HB) method to expeditiously evaluate the periodic responses of nonlinear systems. By employing the fast Fourier transform (FFT) technique, it rapidly computes harmonic expansion coefficients of the nonlinear terms and their corresponding constant tensor matrices. Notably, the nonlinear part of the Jacobian matrix is just the product of the coefficients and the constant tensor matrices, loop computations are no longer requisite for calculating the Jacobian matrix. This, facilitates accelerated determination of the nonlinear portion of the Jacobian matrix, thus obtaining the periodic responses of the system in an efficient manner. Furthermore, the constant tensor matrices are exclusively contingent upon the harmonic bases of the system's periodic response, devoid of reliance on the equation's specific formulation, facilitates obtaining the Jacobian matrix in a general manner. Simulation results on a 20-degree-of-freedom nonlinear oscillator chain system demonstrate that the efficiency of the GE-HB method is about tenfold that of the harmonic balance-alternating frequency/time domain (HB-AFT) method and twenty-fivefold that of the fourth-order Runge-Kutta (RK4) method. Further, the simulation of a 284-degree-of-freedom nonlinear rotor system exhibits the GE-HB method's computational efficiency surpassing HB-AFT method by over 500 times and Newmark method by over 3000 times. Moreover, in these two examples, the GE-HB method captures all solution branches, including unstable periodic solutions, providing comprehensive insights into periodic responses of the systems. The GE-HB method proposed here has the potential to explore dynamic characteristics for high-dimensional complex nonlinear systems in engineering. [Display omitted] [ABSTRACT FROM AUTHOR]

In this paper we investigate the bifurcations and the chaos of a piecewise linear discontinuous (PWLD) system based upon a rig-coupled SD oscillator, which can be smooth or discontinuous (SD) depending on the value of a system parameter, proposed in [18] , showing the equilibrium bifurcations and the transitions between single, double and triple well dynamics for smooth regions. All solutions of the perturbed PWLD system, including equilibria, periodic orbits and homoclinic-like and heteroclinic-like orbits, are obtained and also the chaotic solutions are given analytically for this system. This allows us to employ the Melnikov method to detect the chaotic criterion analytically from the breaking of the homoclinic-like and heteroclinic-like orbits in the presence of viscous damping and an external harmonic driving force. The results presented here in this paper show the complicated dynamics for PWLD system of the subharmonic solutions, chaotic solutions and the coexistence of multiple solutions for the single well system, double well system and the triple well dynamics. [ABSTRACT FROM AUTHOR]

The transient impulses are one of the most important features for the defective bearing diagnosis. Many methods like the envelope analysis are created to analyze the fault-induced impulse. The situation is however different for high-speed bearing-rotor systems whose rotor runs in flexible bearing supports such as aero-engines and gas-turbines, as the impulsive responses are affected by resonance characteristics and rotor eccentric excitation. Few scholars pay attention to the phenomena, since one speed is usually chosen for dynamics or diagnosis in the state-of-the-art research. In this work, a symmetrical rigid bearing-rotor system running in flexible bearing supports was modeled. The influence of the resonance characteristics and rotor eccentric excitation on the fault characteristic frequencies was analyzed via envelope analysis performing on the dynamic response from the numerical simulation at different speeds. Besides, the contrast of the fault characteristic frequencies demonstrated the favorable and unfavorable influence of the resonance characteristics and the rotor eccentric excitation on the quality of the bearing fault vibration signal in different speed ranges, respectively. Accordingly, the mechanisms were explained by analysis of the resonance characteristics and bearing contact force of the system. Finally, the influence of the resonance characteristics was qualitatively verified by the experimental results. • High-speed has unfavorable effects on the impulsive transients and diagnostic results. • The influence of dynamic characteristics on the impulsive transients is discussed in detail. • A strategy for bearing signal enhancement based on dynamic characteristics is proposed. [ABSTRACT FROM AUTHOR]

Abstract: The subharmonic bifurcation and universal unfolding problems are discussed for an arch structure with parametric and forced excitation in this paper. The amplitude–frequency curve and some dynamical behavior have been shown for this class of problems by Liu et al. Here, by means of singularity theory, in the case of strict 1:2 internal resonance, the bifurcation behavior of the amplitude with respect to a parameter (which is related to the amplitude of the live load imposed on the arch structures) is studied. The results indicate that it is a high codimensional bifurcation problem with codimension 5, and the universal unfolding is given. From the mechanical background, 20 forms of two parameter unfoldings with some constraints are studied. The transition sets in the parameter plane and the bifurcation diagrams are plotted. The results obtained in this paper present some new dynamic buckling patterns and abundant bifurcation phenomena. [Copyright &y& Elsevier]

• CMS-POD two-level model reduction is proposed by combining CMS and POD methods. • The dynamic model of dual rotor-bearing system based on FEM for three types of beam elements. • The second-level model reduction has a better computational precision by mode expansion. • The dynamic behaviors of the dual rotor-bearing system are very complicated for a large clearance. In this paper, a dynamic model of a complex dual rotor-bearing system of an aero-engine is established based on the finite element method with three types of beam elements (rigid disc, cylindrical beam element and conical beam element), as well as taking into account the nonlinearities of all of the supporting rolling element bearings. To rapidly and accurately analyze dynamic behaviors of the complex dual rotor-bearing system, a two-level model order reduction (MOR) method is proposed by combining component mode synthesis (CMS) method and proper orthogonal decomposition (POD) technique. The first-level reduced-order model (ROM) of the dual rotors is obtained by CMS method with a high precision for the original system. Then, the POD method is applied to second-level model order reduction to further decrease the degrees of freedom (DOFs) of first-level ROM. Second-level ROM with mode expansion and direct second-level ROM are obtained, and the nonlinear displacement responses of the two ROMs are compared with the first-level ROM. The numerical results demonstrate that the proposed method has a higher computational efficiency and accuracy in terms of mode expansion than the direct model reduction by using POD method. In addition, the nonlinear vibration responses of the dual rotor-bearing system are studied by this second-level ROM in the case of different clearances of the inter-shaft bearing. The results indicate that the dynamic characteristics of the dual rotor-bearing system are very complicated for a large clearance. [ABSTRACT FROM AUTHOR]

Highlights • A force model for the inter-shaft bearing with a local defect on surface of the outer or inner race. • The system may resonant in some non-critical-speed region due to the local defect. • Parameters affecting the resonant frequencies and vibration amplitudes of the abnormal resonances. • A comprehensive parametric analysis is carried out to show the nonlinear resonant response characteristics. Abstract This paper presents a force model for the inter-shaft bearing with a local defect on the surface of the outer race or the inner race, and the nonlinear dynamic characteristics of a dual-rotor system affected by the local defect are investigated. A simplified dual-rotor system is presented with the consideration of the inter-shaft bearing's nonlinearities such as the Hertzian contact force and the radial clearance. The local defect is considered as a regular dent with a constant depth, thus the radial clearance will increase when rolling elements go through the range of the local defect. The motion equations of the system with eight degrees of freedom are formulated by using the Lagrange's equation. The nonlinear vibration responses of the dual-rotor system affected by the local defect are obtained using numerical method. The results show that there exist four abnormal resonances on the amplitude frequency curves of the system due to the effect of the local defect, apart from the couple of primary resonances excited by the unbalance excitations of the two rotors. With the aid of the characteristic defect frequency analysis, it is revealed that one pair of the abnormal resonances are excited by the characteristic defect frequency, and the other pair of the abnormal resonances are excited by the combination frequency. Furthermore, a comprehensive parametric analysis is carried out to give an insight into the nonlinear resonant response characteristics affected by parameters such as the depth and the span of the defect, the rotation speed ratio, the unbalances of two rotors, the stiffness and the damping of the linear elastic spring, and the radial clearance, the stiffness and the roller number of the inter-shaft bearing. The results show that the vibration amplitudes for the abnormal resonances are mainly determined by the depth and the span of the defect, while the resonant frequencies for the abnormal resonances are mainly influenced by the rotation speed ratio and the roller number of the inter-shaft bearing. However, the rotors' unbalances mainly affect the corresponding primary resonance rather than the abnormal resonances. The obtained results will contribute to a better understanding of the nonlinear resonant response characteristics of dual-rotor systems with a local defect on the inter-shaft bearing, which are helpful for the fault diagnostics of the inter-shaft bearing in a dual-rotor system. [ABSTRACT FROM AUTHOR]

Abstract This paper investigates the nonlinear bending of graphene nanoplatelet (GPL) reinforced laminated composite quadrilateral plates using the element-free IMLS-Ritz method. The effective material properties including Young's modulus, mass density and Poisson's ratio are determined by the modified Halpin-Tsai model and rule of mixture. The first-order shear deformation theory (FSDT) and the IMLS-Ritz approximation are employed to obtain the discrete nonlinear governing equation of quadrilateral plates with large deformation. The Newton-Raphson method is used to solve the nonlinear equation. The accuracy of the IMLS-Ritz results is examined by comparing with the published values. A comprehensive parametric study is carried out, with a particular focus on the effects of geometric parameters of quadrilateral plates and GPLs distribution pattern, weight fraction, total number of layers, and geometry and size of GPLs on the nondimensional deflection of GPLs reinforced laminated composite quadrilateral plate. [ABSTRACT FROM AUTHOR]

This paper investigates free vibration of graphene nanoplatelet (GPL) reinforced laminated composite quadrilateral plates using the element-free IMLS-Ritz method. The effective material properties including Young's modulus, mass density and Poisson's ratio are determined by the modified Halpin–Tsai model and rule of mixture. The first-order shear deformation theory (FSDT) is employed for formulation of the energy functional. Based on the IMLS-Ritz approximation, the discrete vibration equation of the laminated composite quadrilateral plates is derived. The accuracy of the IMLS-Ritz results is examined by comparing with the published values. A comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern, geometry and size of GPL reinforcements, total number of layers and geometric parameters of quadrilateral plates on the natural frequencies of GPL reinforced laminated composite quadrilateral plate. [ABSTRACT FROM AUTHOR]

For a local defect modeling in a defective bearing–rotor system, there mainly exist two types of commonly-used models. One is a description of the geometrical boundary simulating a real local defect (GB model), while the other one is a depiction of the consequence —the pulse force produced by a rolling element striking the local defect (PF model). Dynamic equations of defective ball bearing–rotor system based on the two local defect models are established. The defective systems depending on the two defect models reflect the similar dynamic characteristics such as the defect frequencies, the primary resonance and the super-harmonic resonance. However, compared to the GB model, the PF model based governing equation is more suitable to be processed by the classical method for nonlinearities which exists in a defective bearing–rotor system. A frequency-domain method —harmonic balance (HB) method which can obtain the semi-analytical solution is utilized to solve the PF model based governing equation and prove the calculation efficiency. Besides, a rigid rotor–ball bearing experiment system is established, the phenomena such as the defect frequencies, resonance and super-harmonic resonances in theoretical analysis reflected together by two defect models are verified qualitatively. Therefore, it can be concluded that the PF model has an advantage over the GB model for the dynamic analysis. Moreover, the discoveries in this paper may supply some clues for diagnosis of a defective rolling bearing system. [ABSTRACT FROM AUTHOR]

• A type of parallel non-concentricity is defined. • The dual-rotor system model with non-concentricity is established. • The envelope curve of the orbit and polar angle difference are discussed. • The relation between the polar angle difference and the phase angles is calculated. • The effects of the non-concentricity phase angle and the offset are discussed. The machining deviation of the positioning hole of the inter-shaft bearing can cause the fault of the non-concentricity of the dual-rotor system. Aiming at the above problem, a type of parallel non-concentricity is defined, the phase angle and the offset of which are utilized to modify the contact force model of the inter-shaft bearing. The results obtained by the Newmark-β method show that the non-concentricity phase angle and the non-concentricity offset will change the amplitude when the dual-rotor system passes the first critical speed. It is observed that there are 2X and 3X frequencies of the rotational speeds of high- and low-pressure rotors and several combination frequencies of the two rotational speeds, in which the subtraction frequency of high- and low-pressure rotors is dominant. With the non-concentricity phase angle changes, the shape of the orbit and the envelope curve of the orbit of high- and low-pressure rotors will shift. The quantitative correspondence between the polar angle difference and the non-concentricity phase angles is discovered, which can be used to diagnose the fault of the non-concentricity of the dual-rotor system. [ABSTRACT FROM AUTHOR]

This paper investigates the flutter characteristics of graphene nanoplatelet (GPL) reinforced laminated composite quadrilateral plates using the element-free IMLS-Ritz method. The modified Halpin-Tsai model and rule of mixture are employed to predict the effective material properties including Young's modulus, mass density and Poisson's ratio. The energy functions of GPL reinforced composite (GPLRC) quadrilateral plates are obtained by the first-order shear deformation theory (FSDT) and first order piston theory. Based on the IMLS-Ritz approximation, the discrete dynamic equation of GPLRC quadrilateral plates is derived. The accuracy of the IMLS-Ritz results is examined by comparing the natural frequencies with those obtained from published values. A comprehensive parametric study is carried out, with a particular focus on the effects of weight fraction, distribution pattern, total number of layers, geometry and size of GPL reinforcements and geometric parameters of quadrilateral plates on the flutter boundary of GPLRC quadrilateral plates. [ABSTRACT FROM AUTHOR]

• RCmvMSDE is proposed to extract features for fault diagnosis. • The method efficiently extracts discriminative features from multivariate signals. • The stability and reliability of the RCmvMSDE are verified by Synthetic signals. • Two diagnosis case studies show the effectiveness and superiority of RCmvMSDE. Accurate and efficient identification of various fault categories, especially for the big data and multisensory system, is a challenge in rotating machinery fault diagnosis. For the diagnosis problems with massive multivariate data, extracting discriminative and stable features with high efficiency is the significant step. This paper proposes a novel feature extraction method, called Refined Composite multivariate Multiscale Symbolic Dynamic Entropy (RCmvMSDE), based on the refined composite analysis and multivariate multiscale symbolic dynamic entropy. Specifically, multivariate multiscale symbolic dynamic entropy can capture more identification information from multiple sensors with superior computational efficiency, while refine composite analysis guarantees its stability. The abilities of the proposed method to measure the complexity of multivariate time series and identify the signals with different components are discussed based on adequate simulation analysis. Further, to verify the effectiveness of the proposed method on fault diagnosis tasks, a centrifugal pump dataset under constant speed condition and a ball bearing dataset under time-varying speed condition are applied. Compared with the existing methods, the proposed method improves the classification accuracy and F-score to 99.81% and 0.9981, respectively. Meanwhile, the proposed method saves at least half of the computational time. The result shows that the proposed method is effective to improve the efficiency and classification accuracy dealing with the massive multivariate signals. [ABSTRACT FROM AUTHOR]