Search

Nonlinear vibration arises everywhere in engineering. So far there is no method to track the exact trajectory of a space fractional nonlinear oscillator; therefore, a sophisticated numerical method is much needed to elucidate its basic properties. For this purpose, a numerical method that combines the Fourier spectral method with the Runge–Kutta method is proposed. Its accuracy and efficiency have been demonstrated numerically. This approach has full physical understanding and numerical access; thus, it can be used to solve many types of nonlinear space fractional partial differential equations with periodic boundary conditions.

In this work, modified designs of Helmholtz resonators with extended deflected neck are proposed, numerically evaluated and optimized aiming to achieve a better transmission loss performance over a broader frequency range. For this, 10 Helmholtz resonators with different extended neck configurations (e.g. the angle between extended neck and the y-axis) in the presence of a grazing flow are assessed. Comparison is then made between the proposed resonators and the conventional one, i.e. in the absence of an extended neck (i.e. Design A). For this, a two-dimensional linearized Navier Stokes equations-based model of a duct with the modified Helmholtz resonator implemented was developed in frequency domain. The model was first validated by comparing its numerical predictions with the experimental results available in the literature and the theoretical results. The model was then applied to evaluate the noise damping performance of the Helmholtz resonator with (1) an extended neck on the upstream side (Design B); (2) on the downstream side (Design C), (3) both upstream and downstream sides (Design D), (4) the angle between the extended neck and the y-axis, i.e. (a) 0°, (b) 30°, and (c) 45°, (d) 48.321°. In addition, the effects of the grazing flow Mach number (Ma) were evaluated. It was found that the transmission loss peaks of the Helmholtz resonator with the extended neck was maximized at Ma = 0.03 than at the other Mach numbers. Conventional resonator, i.e. Design A was observed to be associated with a lower transmission loss performance at a lower resonant frequency than those as observed on Designs B–D. Moreover, the optimum design of the proposed resonators with the extended neck is shown to be able to shift the resonant frequency by approximately 90 Hz, and maximum transmission loss could be increased by 28–30 dB. In addition, the resonators with extended necks are found to be associated with two or three transmission loss peaks, indicating that these designs have a broader effective frequency range. Finally, the neck deflection angles of 30° and 45° are shown to be involved with better transmission loss peaks than that with a deflection angle of 0°. In summary, the present study sheds light on maximizing the resonator’s noise damping performances by applying and optimizing an extended neck.

A new method of removing waste chips is proposed by focusing on the key factors affecting the processing quality and efficiency of high energy beams. Firstly, a mathematical model has been established to provide the theoretical basis for the separation of solid–liquid suspension under ultrasonic standing wave. Secondly, the distribution of sound field with and without droplet has been simulated. Thirdly, the deformation and movement of droplets are simulated and tested. It is found that the sound pressure around the droplet is greater than the sound pressure in the droplet, which can promote the separation of droplets and provide theoretical support for the ultrasonic suspension separation of droplet; under the interaction of acoustic radiation force, surface tension, adhesion, and static pressure, the droplet is deformed so that the gas fluid around the droplet is concentrated in the center to achieve droplet separation, and the droplet just as a flat ball with a central sag is stably suspended in the acoustic wave node.

Conventional metallic sandwich panels are widely used for noise control owing to their good noise control capabilities and excellent mechanical strength-to-weight ratio property. Furthermore, sound-absorbing products consisting of glass or mineral fiber materials are generally filled into the sandwich structures to lower the vibration response in resonance frequency and to enhance the structural noise attenuation capacity. In the present study, a fiber-reinforced graphite material is used as an alternative to its metallic counterparts. Moreover, a wood-based renewable absorption material is used as the absorption material and is filled into the sandwich structural core. The vibro-acoustic characteristics of the panel with such a design are numerically investigated using Actran. The findings of the research indicate that the proposed sandwich structure achieves advanced low-frequency noise control performance in comparison with other conventional metallic sandwich panels. Approximately 7 dB increase in sound transmission loss in the audible-frequency range is achieved in addition to a reduced panel weight and more stable vibration with reduced amplitude. The existing data available in the literature are employed for validating and illustrating the accuracy and reliability of the proposed approach.

The success of the unscented Kalman filter can be jeopardized if the required initial parameters are not identified carefully. These parameters include the initial guesses and the levels of uncertainty in the target parameters and the process and measurement noise parameters. While a set of appropriate initial target parameters give the unscented Kalman filter a head start, the uncertainty levels and noise parameters set the rate of convergence in the process. Therefore, due to the coupling effect of these parameters, an inclusive approach is desired to maintain the chance of convergence for expensive experimental tests. In this paper, a framework is proposed that, via a virtual emulation prior to the experiment, determines a set of initial conditions to ensure a successful application of the online parameter identification. A Bayesian optimization method is proposed, which considers the level of confidence in the initial guesses for the target parameters to suggest the appropriate noise covariance matrices. The methodology is validated on a five-story shear frame tested on a shake table. The results indicate that, indeed, a trade-off can be made between the robustness of the online updating and the final parameter accuracy.

A new dynamical model with five rigid frames (RFs), driven by two counter-rotating exciters, is proposed to explore the synchronization, stability, and motion characteristics of the system in this paper. The motion differential equations and the corresponding responses of the system are given firstly. Using the average method, the average torque balance equations for the two exciters are deduced. According to the relationship between the difference of the dimensionless effective output electromagnetic torques for the two motors and the coupling torques of the system, the theory condition of realizing synchronization is obtained. Based on the Hamilton’s theory, the theory condition of stability of the system is deduced. The stability and motion characteristics of the system for different resonant regions are qualitatively discussed in numeric, including the stable phase difference of the two exciters, relative phase relationships among the five rigid frames, amplitude-frequency characteristics, stability coefficients, and the effective load torque between the two exciters. Simulations are carried out to further quantitatively validate the feasibility of the above theoretical and numerical qualitative results. It is shown that in engineering the reasonable working points of the system should be selected in Region II, only in this way, can the synchronous and stable relative linear motion of the system with the zero stable phase difference in vertical direction be realized, and in this case, the vibrations of the four inner rigid frames (IRFs) in the horizontal direction are compensated with each other, and the energy is also saved due to utilizing the resonant effect. Based on the present work, some new types of vibrating coolers/dryers or vibrating screening machines can be designed.

Lithium-ion batteries are being increasingly used as the main energy storage devices in modern mobile applications, including modern spacecrafts, satellites, and electric vehicles, in which consistent and severe vibrations exist. As the lithium-ion battery market share grows, so must our understanding of the effect of mechanical vibrations and shocks on the electrical performance and mechanical properties of such batteries. Only a few recent studies investigated the effect of vibrations on the degradation and fatigue of battery cell materials as well as the effect of vibrations on the battery pack structure. This review focused on the recent progress in determining the effect of dynamic loads and vibrations on lithium-ion batteries to advance the understanding of lithium-ion battery systems. Theoretical, computational, and experimental studies conducted in both academia and industry in the past few years are reviewed herein. Although the effect of dynamic loads and random vibrations on the mechanical behavior of battery pack structures has been investigated and the correlation between vibration and the battery cell electrical performance has been determined to support the development of more robust electrical systems, it is still necessary to clarify the mechanical degradation mechanisms that affect the electrical performance and safety of battery cells.

The low-frequency harmonic components of urban substation noise are easy to annoy the residents. Multi-frequency perfect sound-absorbing metasurface based on the Helmholtz resonator (HR) is an alternative solution to suppress the low-frequency harmonic noise. This paper proposes an efficient design method of structural parameter for the multi-frequency perfect sound-absorbing metasurface. Taking the perfect sound absorption at the target frequency as objective and the structural parameters of HR as optimization variables, the structural parameter optimization model of multi-frequency perfect sound-absorbing metasurface is established and solved by the sequential quadratic programming algorithm. The proposed design method effectively overcomes the deterioration of sound absorption performance caused by the combined design of multiple perfect sound absorption units. Utilizing the proposed method, we designed a multi-frequency perfect sound-absorbing metasurface to absorb the four harmonic components of an urban substation noise simultaneously. The finite element simulation results and the experimental results of the physical sample indicate that the designed multi-frequency perfect sound-absorbing metasurface can satisfy critical coupling to achieve perfect sound absorption at all target frequencies.

In this paper, a synchronous vibration control method was proposed to avoid the high-cycle fatigue fracture of aeroengine rotor blade. Firstly. The harmonic force, causing synchronous vibration, was derived by Fourier series expansion by the mean of simplifying the aerodynamic exciting forces into the periodic rectangular pulse wave forces. It was found that the synchronous vibration can be controlled by adjusting the primary excitation forces parameters. Based on this, the additional secondary excitation forces were introduced to control the synchronous vibration caused by primary excitation forces. Secondly, the influences of the number, position, direction, duration of additional secondary excitation forces and the phase difference between additional secondary excitation forces and primary excitation forces on the synchronous vibration control were obtained through theoretical analysis, which was simulated and verified by a single-degree-of-freedom model. Thirdly, a high-speed straight blade test bench was established, and the feasibility of the method in controlling synchronous vibration of rotor blade was proved by adding additional magnet excitation forces on the basis of fixed magnet excitation forces. Finally, the suppression strategy of synchronous vibration of rotor blade by introducing additional secondary excitation forces was given. It can provide theoretical and technical support for effectively controlling the synchronous vibration amplitude and avoiding the high-cycle fatigue fracture of rotor blade in engineering practice.

A high-speed-level gear transmission system model of a wind turbine is presented considering a time-varying wind load and an electromagnetic torque disturbance, along with eccentricity, dynamic backlash, and friction force. The auto-regressive model is employed for simulating the time-varying wind load in the realistic wind field as external excitation. A doubly fed induction generator model of the wind turbine is established to calculate the disturbance quantity of electromagnetic torque. The nonlinear differential equations of the system are strictly deduced using Lagrange equation and solved by the fourth-order Runge-Kutta method. The effect of friction on the dynamic response of the high-speed-level gear transmission system is analyzed with the time-varying wind load and the electromagnetic torque disturbance. These results show that the friction force is critical because frequency amplitude and components can be changed by it. The friction force also enlarges vibration displacement. The low-frequency components in the vertical direction are affected gravely by the friction force without electrical disturbance. In addition, sidebands exist in the vicinity of the low-frequency parts as the electromagnetic torque disturbance appears at the output end. The amplitude of the low-frequency component is further increased because of electromagnetic torque disturbance. This shows the frequency characteristics of the slight gear system fault. The study offers some fresh references into the design and diagnosis of the gear system.

In this paper, the nonlinear vibration of railway track systems resting on elastic foundation has been studied. An axially loaded simply supported Euler–Bernoulli beam resting on a flexible foundation has been considered to provide a mathematical representation of the railway track system. Winkler springs have been used to model the elastic foundation. Nonlinear partial differential equation of the system has been presented and solved. A new approximate analytical solution called Improved Amplitude–Frequency Formulation (IAFF) is proposed to obtain nonlinear frequency of the system and an accurate analytical solution for the whole domain. The first iteration of the IAFF leads to a highly accurate solution in comparison with the exact frequency of the problem. The exact frequency of the problem is also presented, and the results of IAFF are compared and verified. Sensitive analysis of the soil stiffness and loading condition is studied for different parameters. A full comparison of the IAFF and exact solution results are illustrated. It has been proved that the IAFF can be potentially extended to highly nonlinear conservative problems.

This paper presents a new drilling tool with multidirectional and controllable vibrations for enhancing the drilling rate of penetration and reducing the wellbore friction in complex well structure. Based on the structure design, the working mechanism is analyzed in downhole conditions. Then, combined with the impact theory and the drilling process, the theoretical models including the various impact forces are established. Also, to study the downhole performance, the bottom hole assembly dynamics characteristics in new condition are discussed. Moreover, to study the influence of key parameters on the impact force, the parabolic effect of the tool and the rebound of the drill string were considered, and the kinematics and mechanical properties of the new tool under working conditions were calculated. For the importance of the roller as a vibration generator, the displacement trajectory of the roller under different rotating speed and weight on bit was compared and analyzed. The reliable and accuracy of the theoretical model were verified by comparing the calculation results and experimental test results. The results show that the new design can produce a continuous and stable periodic impact. By adjusting the design parameter matching to the working condition, the bottom hole assembly with the new tool can improve the rate of penetration and reduce the wellbore friction or drilling stick-slip with benign vibration. The analysis model can also be used for a similar method or design just by changing the relative parameters. The research and results can provide references for enhancing drilling efficiency and safe production.

Vibrations contribute to helicopter’s ride comfort. This study aimed to determine the relationship between main rotor vertical excitations and discomfort. Fifty-three participants, seated on a helicopter seat fixed to a vibration test bench, evaluated the discomfort of vertical sinusoidal vibrations using a magnitude estimation procedure. Stimuli had a frequency between 15 and 30 Hz and a level between 0.32 and 3.16 m/s2. The average discomfort was shown related to vibration velocity using Steven’s power law, without any frequency dependence. The exponent depended on velocity and was 1.18 for higher velocities (approx. above 0.008 m/s) and 0.65 for velocities below that limit.

The vibration dissipation mechanism of the rotating blade with a dovetail joint is studied in this paper. Dry friction damping plays an indispensable role in the direction of vibration reduction. The vibration level is reduced by consuming the total energy of the turbine blade with the dry friction device on the blade-root in the paper. The mechanism of the vibration reduction is revealed by the variation of the friction force and the energy dissipation ratio of dry friction. In this paper, the flexible blade with a dovetail interface feature is discretized by using the spatial beam element based on the finite element theory. Then the classical Coulomb-spring friction model is introduced to obtain the dry friction model on the contact interfaces of the tenon-mortise structure. What is more, the effects of the system parameters (such as the rotating speed, the friction coefficient, the installation angle of the tenon) and the excitation level on blade damping characteristics are discussed, respectively. The results show that the variation of the system parameters leads to a significant change of damping characteristics of the blade. The variation of the tangential stiffness and the position of the external excitation will affect the nonlinear characteristics and vibration damping characteristics.

Pull-in instability occurs in a micro-electromechanical system, and it greatly hinders its normal operation. A fractal modification is suggested to make the system stable in all operation period. A fractal model is established using a fractal derivative, and the results show that by suitable fabrication of the micro-electromechanical system device, the pull-in instability can be converted into a novel state of pull-in stability.

This paper presents a robust control methodology based on a disturbance observer and an optimal states feedback for Takagi–Sugeno fuzzy system. Firstly, the nonlinear systems were solved by applying a sector nonlinearity method to get the inner linear subsystems and outer fuzzy membership functions, which guaranteed the conversion without any loss generality characteristics of the system. Secondly, an exponentially convergent disturbance observer was constructed to the system with an assumption that the system states are temporarily bounded. Thirdly, a states observer was built by poles placement of linear quadratic regulation optimization, which was used to place the system states error poles located on the stable region. Finally, simulation examples were given to figure out that the proposed controller is effective to control the Takagi–Sugeno fuzzy system. The obtained results are disturbance mostly rejected, state estimation errors are quite small, and the output signal precisely tracked input signal.

The present work deals with a study of a nonlinear singular oscillator. To approximate the frequency–amplitude relationship of the singular oscillator, reproducing kernel method is employed. The approximate solution is compared with the exact solution as well as the results obtained by the He’s frequency–amplitude formulation, to show the effectiveness of the proposed technique for solving the problem.

A time-delayed acceleration feedback control is proposed to improve the vibration performance of a nonlinear vehicle suspension system. First, the harmonic balance method is applied to obtain the vertical acceleration amplitude of the system excited by simple harmonic road excitation. Then, taking the amplitude of the sprung mass acceleration and control force into account, the single-objective and multiple-objective optimization problems of time-delayed feedback control parameters, respectively, are discussed. Finally, the mathematical simulation is provided to verify the correctness of the optimization results. It is concluded that the nonlinear suspension with optimal time-delayed feedback control has better vibration control performance compared to passive one. The acceleration amplitude of the sprung mass is significantly reduced by the single-objective optimization of the control parameters. Moreover, when the optimal time delay is introduced, the active control force input is fewer than that without time delay. The phenomenon of energy transfer between the sprung mass and the unsprung mass is observed in some road-excitation frequencies.

Recently, an analytical solution of a quadratic nonlinear oscillator has been presented based on the harmonic balance method. By introducing a small parameter, a set of nonlinear algebraic equations have been solved which usually appear among unknown coefficients of several harmonic terms. But the method is not suitable for all quadratic oscillators. Earlier, introducing a small parameter to the frequency series, Cheung et al. modified the Lindstedt–Poincare method and used it to solve strong nonlinear oscillators including a quadratic oscillator. But due to some limitations of both parameters, a changed form of frequency-related parameter (introduced by Cheung et al.) has been presented for solving various quadratic oscillators.

For interfacial stratification mechanism of sandwich plate structures, the forced propagation solution of interface shear stress excited by SH waves is derived by global matrix methods and integral transformation methods. The necessary condition of interfacial shear delamination excited by alternating stress is analyzed with the interface fatigue failure theory. The exact value of forced propagation solution is calculated by adaptive Gauss–Kronrod quadrature numerical integration methods, which is verified via finite element methods. The coupling resonance mechanism of interface shear stratification is revealed by the forced vibration solution and the mass-spring model. The effects of excitation frequency, structural parameters, accretion, and matrix materials on the interfacial shear delamination are analyzed and discussed by practical cases of vibration de-accretion. For interface shear stratification of sandwich structures, the optimal excitation frequency as well as substrate thickness and accretion thickness is the value at coupling resonance, around which the interfacial shear stratification interval is formed by the interface fatigue failure criteria. In the stratification or/and antistratification design excited by vibrations, the excitation source and structure could be optimized by the method. Therefore, the results have important theoretical value for the extension and application of vibration stratification or/and antistratification technology.

In recent years, the research of nonlinear energy sink on low-frequency noise control has become a hotspot. By adding a nonlinear energy sink into one primary system, it is possible to obtain the significant target energy transfer characteristics. The target energy transfer can be defined for which the vibration energy of the primary structure is irreversibly transferred to the nonlinear energy sink, quickly concentrated in the nonlinear energy sink and dissipated by the nonlinear energy sink damping. This method has significant advantages to control the broadband low-frequency noise inside the transportations (such as cars, trains, airplanes, etc.). Compared with traditional noise reduction methods such as adding the damping and acoustical materials, the nonlinear energy sink has a simple and lightweight structure. The paper reviews the nonlinear characteristics of the nonlinear energy sink, the main theoretical research methods and the applications of vibration and noise control, and discusses the application of the nonlinear energy sink for the control of low-frequency noise inside the three-dimensional acoustic cavities, which provides the reference and guidance for the low-frequency noise control inside the acoustic cavities of the mean of transportation.

The principal aim of this paper is to analyze the impact of rubber pad systems on levels of vibrations and values of stresses and deformations induced in the subway tunnel segments. Thus, the 3D model has been selected to be isotropically simulated in the ANSYS program to conduct a finite element analysis. Therefore, the proposed track system in the tunnel of line 4 of the Greater Cairo Metro has been selected as an analytical and simulation case study. The impact of using eight different values for the stiffness of the rubber pad system in the case of a single tunnel has been analyzed. The results showed that levels of vibrations are significantly affected and are in logarithmic correlation with the stiffness. Also, the impact of the stiffness on the deformations and stresses are determined as well as mathematical models connecting the different parameters have been introduced.

Blade crack will cause severe mistuning of hard-coated blisks, which will lead to vibration localization. To identify crack mistuning and analyze influence factors, in this study, a mistuning identification method of blade cracks in hard-coated blisks is presented based on modified component mode mistuning reduced-order model, in which the hard-coated blisk with blade crack is decomposed into a substructure of tuned hard-coated blisk and a substructure of coated blade with cracks. Crack mistuning of each coated blade can be obtained by a single identification calculation. After verifying the rationality of this identification method, the influence factors of blade crack mistuning are analyzed. The influence factors include the crack location on the coated blade (cracks occurring only in coating or only in blade substrate or both in blade substrate and coating), crack length, crack position in the radial direction of the blisk, and modal data type of coated blisk used for mistuning identification calculation. The research results show that, with the increase of crack length, the mistuning of crack occurring only in the coating does not increase continuously but decreases firstly and then increases. For the first bending modes, the closer the blade crack is to the blade root, the larger the mistuning is. For the second bending modes, the blade crack located at the position of maximum modal displacement will produce large mistuning. For hard-coated blisk with blade crack, these crack mistuning variation rules are of great significance to the dynamic analysis and the determination of the crack location.

Due to the frequently occurred adverse vibration of hydraulic structures, vibration risk assessment is significant for the water energy efficiency of hydropower station and the safety of people and structures. Recently, the abnormal vibration of hydro-turbine-generator in a large hydropower station occurred and the main influencing factors of vibration are analyzed based on the prototype data and engineering experience. Different from the deterministic variable features in traditional support vector domain description (SVDD) algorithms, the feature of vibration amplitude is actually a random variable so that the different target objects will be obtained at different confidence levels. In order to assess the vibration range and excessive vibration probability, the original SVDD boundary at relatively low confidence level is firstly calculated. Then, the boundary extension operation with detailed theoretical deduction is performed and the extended boundary is further optimized inspired by path planning problem. The advantage of proposed approach is that it can improve the data fitting performance for single dimension (i.e. vibration amplitude) without leading to complex boundary which cannot be used for vibration risk assessment. By applying this approach to the practical vibration problem, the quantitative and slightly conservative assessment results are conveniently obtained, which indicate that this approach is reasonable and cost-effective.

The high-static-low-dynamic stiffness vibration isolator has great advantages in vibration isolation because it can decrease the natural frequency of the system while keeping the load capability, but it is usually difficult to implement because of its complex structures and installation space constraints. A high-static-low-dynamic stiffness vibration isolator composed of a buckling circular plate and a traditional linear spring is proposed in this paper. The buckling circular plate works as the negative stiffness corrector paralleled with the linear spring, which can be integrated into the sleeve. If the load is chosen properly, the static equilibrium point will be at the initial quasi-zero stiffness point. However, any changes of the load will lead the equilibrium point deviating from the initial equilibrium point. The nonlinear mathematical model of high-static-low-dynamic stiffness vibration isolator considering load imperfection is developed and its force transmissibility is analyzed with the harmonic balance method and homotopy perturbation method. The influence rule of the system parameters on it is analyzed and the corresponding results show that the force transmissibility will exhibit complicated characteristics, depending on the load imperfection, damper, and excitation force.

Inerter, a new type of mass element, can increase the inertia of motion between two endpoints. In order to study the dynamic inertia effect of inerter–spring–damper suspension for heavy vehicle on ride comfort and road friendliness, the inerter–spring–damper suspension is applied and its mechanism is studied. This paper establishes a half vehicle model of inerter–spring–damper suspension for heavy vehicle. The parameters of inerter–spring–damper suspension for heavy vehicle are optimized by multi-objective genetic algorithm and system simulations are carried out. The parametric influence of different spring stiffness, damping coefficient, inertance, and load on suspension performance is also studied. The simulation results demonstrate that the centroid acceleration and pitch angular acceleration are improved by 24.90% and 23.54%, respectively, and the comprehensive road damage coefficient is reduced by 4.05%. The results illustrate that the inerter–spring–damper suspension can decrease the vertical vibration of vehicle suspension especially in low frequency and reduce the road damage. The analyses of suspension parameters perturbation reveal their different effect laws of the different wheels on vehicle ride comfort and road friendliness, which provide a theoretical basis for setting parameters of inerter–spring–damper suspension.

The parameters of the monorail bridge, which have a significant effect on the vehicle, are analyzed in this paper. With Park method, a complicated solver of the second order with a variable step size, equations insolvable to traditional methods can be solved and a more complicated dynamic model could be built. Different from some traditional simulation of vehicle–bridge coupling system, the bridge is divided into the girder and piers. The finite element model of each part is created separately in Ansys and coupled with the vehicle system in UM, which helps the analysis of the interaction forces between flexible components and better simulation accuracy can be obtained. FIALA model is used to calculate the wheel force. These methods make the measurement more precise. The study shows that all the variables except for the stiffener thickness have little effect on the vibration of the vehicle due to the good vibration reduction performance of the vehicle system. The resonance of the girder could be avoided by changing the thickness of the stiffeners and web plates. In addition, high stiffness and damping of the connection point of the girder and pier are helpful in alleviating the vibration of the bridge.

This study investigates the vibration control issue of active suspension systems. Unlike previous results that neglect the actuator dynamics or consider the impractical symmetrical hydraulic cylinder model, this paper incorporates more reasonable asymmetric electrohydraulic actuator into active suspension system and derives its dynamic model. However, whether active suspension or electrohydraulic actuator suffers from nonlinearities (e.g. nonlinear spring, nonlinear damper and nonlinear actuator dynamics) and parameters uncertainties (e.g. the variations of sprung mass and hydraulic fluid’s bulk modulus as well as hydraulic cylinder original control volumes) , which were rarely synthetically considered in the existing researches.To address these issues, we develop a novel dual adaptive robust controller (ARC). An ARC is firstly designed for main-loop system for stabilizing the car body and improving ride comfort in the presence of nonlinearities and parameter uncertainties as well as road disturbances. In order to meet the constraints requirements of suspension system, the tunable parameters in main-loop control law are optimized by solving linear matrix inequality with kidney-inspired algorithm. Another ARC is further synthesized for sub-loop system to deal with the nonlinear and uncertain dynamics in electrohydraulic actuator for ensuring the force tracking performance. Meanwhile, the uncertain parameters are estimated online to compensate the model deviation. The terminal control law is able to guarantee the asymptotic stability of close-loop system within Lyapunov framework. Finally, the effectiveness and robustness of the proposed controller are demonstrated via excessive simulation experiments over different road conditions.

This paper carries out the transient behaviors of a thin rectangular plate considering different boundary conditions, Pasternak foundation, and thermal environment simultaneously. The governing differential equations of the system are derived by employing the Kirchhoff’s classical plate theory and Hamilton’s principle. This paper proposes a novel semi-analytical methodology, which integrates Laplace transform, the one-dimensional differential quadrature method, Fourier series expansion technique, and Laplace numerical inversion to analyze plates’ transient response. The proposed method can obtain dynamic response of the rectangular efficiently and accurately, which fills the gap of transient behaviors in semi-analytical method. A comparison between semi-analytical results and numerical solutions from the publication on this subject is presented to verify the method. Specifically, the results also agree well with the data generated by the Navier’s method. The convergence tests indicate that the semi-analytical algorithm is a quick convergence method. The effects of various variables, such as geometry, boundary conditions, temperature, and the coefficients of the Pasternak foundation, are further studied. The parametric studies show that geometry and temperature change are significant factors that affect the dynamic response of the plate.

This paper presents investigations into a comparative assessment of the effects of low- and high-frequency noise in relation to personality traits. The high- and low-frequency noises used are produced in the research laboratory using CoolEdit software. In all, 80 candidates were exposed to equivalent continuous sound pressure level of 65 dBA of low- and high-frequency noise in an acoustic room with a 2-week interval. After 1 hour of exposure to noise, participants were asked to complete noise annoyance scale, Weinstein noise sensitivity questionnaire and loudness perception. The results obtained indicate that there is a significant difference between annoyance and perception of low-frequency noise in comparison to annoyance and perception of high-frequency noise, but no significant difference is noted between sensitivity to low- and high-frequency noise. The multivariate analysis of covariance test is applied, which reveals that personality traits have a significant effect on sensitivity to low- and high-frequency noise, annoyance due to low- and high-frequency noise, loudness perception of low-frequency noise, but no interaction effects are found. It is further shown that personality traits are more effective on sensitivity, annoyance and loudness perception to high-frequency noise than those of low-frequency noise, and such effects are not only influenced by severity of noise but also by personality traits and frequency components.

Existing approaches to reducing the low-frequency noise exposure of dwellings are not always sufficient. This study investigated the significance of dwelling layout design for low-frequency noise control. The sound distribution in six typical Chinese dwelling layouts was analysed using in-situ measurements under steady-state noise of various low frequencies. The results showed that among two-bedroom dwelling layouts, the overall average noise reduction varied considerably (6 dB). The noise reduction for room levels (number of rooms sound crosses) 1–2 and 2–3 varies by 5 and 3 dB, respectively, and the noise reduction at door openings varies by 5 dB. A model to approximate the low-frequency noise reduction of a layout was developed using the polyline distance from the noise source and the number of walls the polyline has to cross, which were clearly shown to influence low-frequency noise reduction and seem to be the strongest investigated factors.

In the paper two types of numerical models of the self-excited acoustical system are presented. This new type of auto-oscillating system is used for stress change measurement in constructions and rock masses. The essence of the self-excited acoustical system is to use a vibration emitter and vibration receiver placed at a distance, which are coupled with a proper power amplifier, and which are operating in a closed loop with a positive feedback. This causes the excitation of the system. The change of the velocity of wave propagation, which is associated with the change of the resonance frequency in the system is caused by the deformation of the examined material. Stress changes manifest themselves in small but detectable variations of frequency. The first of the presented models was created on the basis of estimating the model parameters by identification of the sensor–conditioner–amplifier–emitter system. The second mathematical model was delivered from the force–charge equation of the piezoelectric transducers: the sensor and the emitter. The model of the loaded beam, which determined the response of any beam point to the force applied to any other beam point is also presented.

This paper couples Li–He’s homotopy perturbation method with the energy method to obtain an approximate solution of a tangent nonlinear packaging system. A higher order homotopy equation is constructed by adopting the basic idea of the Li–He’s homotopy perturbation method. The energy method is used to improve the maximal displacement and the frequency of the system to an ever higher accuracy. Comparison with the numerical solution obtained by the Runge–Kutta method shows that the shock responses of the system solved by the new method are more effective with a relative error of 0.15%.

The nonlinear vibration effect of nanobeam and problem of the pull-in between the nanobeam and driven plate are the factors which prevent nano-resonator from improving the performance. The nonlinear governing differential equation is built by considering the axial force with piezoelectric controller. The piezoelectric time-delay electrostatic pull-in control is studied and the first-order approximate solution of nonlinear equation is gotten by using the method of multi-scale. The amplitude–frequency and phase frequency response equation of nonlinear vibration system are given for the primary resonance response of the nanobeam. The relationship between the control effect and feedback control parameters is studied. It is found that the piezoelectric time-delay control can change the critical voltage but not the critical position. The axial force can affect the performance of nanobeam.

In this paper, a modified harmonic balance method is presented to solve nonlinear forced vibration problems. A set of nonlinear algebraic equations appears among the unknown coefficients of harmonic terms and the frequency of the forcing term. Usually a numerical method is used to solve them. In this article, a set of linear algebraic equations is solved together with a nonlinear one. The solution obtained by the proposed method has been compared to those obtained by variational and numerical methods. The results show good agreement with the results obtained by both methods mentioned above.

A stability analysis for a smart beam with an adaptive controller is presented in the paper when considering the time delay phenomenon. With the Lagrange equation and the assumed modes method, a dynamical model is constructed to describe the hysteresis nonlinearity of the smart beam. By simulation and experiment, the nonlinear model is proved effectively using the strain response near the root of the beam when the piezoelectric actuator is applied on with a chirp voltage. Based on the dynamical model, a stability analysis method is proposed with an eigenmatrix in the discrete control system. Through some simulation verifications, it is concluded that a proper time delay will be useful to improve the stability of the smart beam with an adaptive controller. Furthermore, it is verified by the experiments that the free vibration amplitude of the smart beam with an artificial time delay 0.05 s is smaller compared with that at no time delay.

Suspension system is one of the important parts of a vehicle, which is used to buffer the impact of uneven road to the body and passengers, so the suspension system has an important impact on the safety and ride comfort of the vehicle. In order to improve the safety and comfort of passengers and vehicles, in this paper a five-degree-of-freedom half car model is established, and the uncertainty of the model and the time-delay of the control are considered. The dynamic response of vehicle body acceleration root mean square, passenger acceleration root mean square, displacement root mean square and vehicle body pitch acceleration root mean square are selected as optimization objectives. The time-delay control parameters are determined by chaos particle swarm optimization algorithm. The time-delay stability of the suspension control system is analyzed by frequency-domain scanning method to ensure the stability of the time-delay control system. Finally, by establishing the simulation model of the active suspension system with double time-delay feedback control, the response characteristics of the suspension system with double time-delay active feedback control to simple harmonic excitation and random excitation input are analyzed. The results show that under the premise of ensuring the system stability, the active suspension system with double time-delay feedback control has good and obvious controlling and damping effect on the body and seats.

As a key component of satellite flexographic printing equipment, the vibration characteristics of the central impression cylinder have an important effect on the product quality. In order to improve dynamic characteristic of the central impression cylinder, the modal analysis on the central impression cylinder is carried out in combination with finite element software in this paper. Then, the modal properties are systematically compared between the central impression cylinder with circulating cooling water and without. The results show that the natural frequency of the central impression cylinder is greatly reduced based on the fluid–solid coupling method. Simultaneously, the natural frequencies and mode shapes of the central impression cylinder based on the finite element analysis are verified by an experimental test. The simulation results are in good agreement with the experimental results, indicating the effectiveness of the finite element model and experimental method used in this study.

In order to reduce the natural frequency of the piezoelectric vibration energy harvester, improve performance of the piezoelectric vibration energy harvester, and meet the requirements of energy acquisition in the low-frequency vibration environment, a variable-section circular piezoelectric vibration energy harvester is presented. The dynamic model and electromechanical coupling model of variable-section circular piezoelectric vibration energy harvester are established. The main factors affecting the output performance of piezoelectric vibration energy harvester are analyzed. The structure parameters of piezoelectric vibration energy harvester are optimized by orthogonal experiment. An experimental platform is built to test output voltage and output power of piezoelectric vibration energy harvester. The experimental results show that when the number of energy harvester is 4 and the external load is 180KΩ, the parallel output power can reach 0.213mW, which can meet the requirements of micro-power device power supply.

Many nonlinear vibrations arising in the engineering of architecture include noise and uncertain properties, and this paper suggests a fractional model to elucidate the properties. The fractional sine-Gordon equation with the Riemann–Liouville fractional derivative is used as an example to solve its periodic solution by the homotopy perturbation method. The frequency–amplitude relationship is obtained, and the effect of the fractional derivative order on the vibration property is discussed. Additionally, the harmonic resonance is also discussed. This preliminary research can be further extended to real applications.

He’s frequency–amplitude formulation and its modifications mainly depend upon the residual calculation. A suitable choice of a residual leads to an ideal result. This paper discusses some effective methods for the residual calculation, and a modification with a free parameter is suggested to effectively estimate the frequency of a nonlinear oscillator. Furthermore, an energy-based residual calculation is also suggested, which is deduced from a variational principle.

The unprecedented frequency formulation proposed by Chinese mathematician, Ji-Huan He, has been caught much attention due to its extreme simplicity and remarkable accuracy for nonlinear oscillators. This short remark uses an example without a linear term arising in ball-bearing oscillating to show its effectiveness and reliability.

It is well documented that active suspension systems offer substantial benefits in ride comfort, handling control over traditional passive systems. However, restrictive features such as the power required and costs make an active system impractical. To solve those problems, semi-active suspension systems have been developed. This paper aims at providing a review of the present state-of-the-art in the semi-active suspension control field in terms of vehicle ride comfort and road-holding performance evaluation. Strengths and weaknesses of the semi-active suspension systems are identified and their relative performance capabilities and equipment requirements are discussed. Furthermore, examples of the current mass market implementation for semi-active suspension systems for road vehicle are discussed.

This paper presents a new dynamic absorber attenuating the vibrations at three resonance frequencies simultaneously. The dynamic vibration responses of mechanical systems with dynamic absorbers are mainly influenced by how close the eigenfrequencies of the installed dynamic absorbers are to the eigenfrequencies of the hosting structure. To suppress structural vibration at single target frequency, it is enough to install a single mass tuned dynamic absorber whose eigenfrequency is tuned to the excitation frequency. To suppress structural vibrations at multiple frequencies, multiple dynamic absorbers whose eigenfrequencies are tuned differently can be installed. Inevitably this approach increases the total weight of the dynamic absorbers and the manufacturing cost. To overcome the limitation and to attenuate vibrations over a wide range of frequencies, a new dynamic absorber without a damper tuned for multiple frequencies was presented in this research. The present dynamic absorber consists of a mass and two arm-beams connected to a hosting structure. By changing the geometric dimensions, it is possible to precisely tune the eigenfrequencies of the dynamic absorbers to those of hosting structure. The present study also adopts an optimization process to tune the geometric parameters based on the numerical optimization algorithm. With several numerical examples and an experiment, the validity of the present dynamic absorber is presented.

To determine the effect of rotor eccentricity on the vibration of multistage pumps, a five-stage centrifugal pump with vaned diffusers was selected to experimentally measure the vibration characteristics under both stable condition and unstable condition due to the rotor eccentricity. The results show that the rotor eccentricity results in an irregular orbit of the rotor axis, which is diffused outward. As the flow rate increases, the peak amplitude of the rotor axis’ orbit first decreases and then increases, and the peak amplitude at the design flow rate is minimized. The main vibration frequencies of rotor axis’ orbit are the axis passing frequency and a secondary high frequency. After rotor eccentricity occurs, all monitoring point vibrations increase by different degrees, the increments of axial vibration are particularly obvious, and the characteristic frequencies of the pump increase.