Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium

An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study.Mechanical properties of MFG porous plates change according to the length,width,and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology.Especially,new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work.Applying Hamilton's principle and the refined higher-order shear deformation plate theory,the governing equation of motion of an MFG porous rectangular plate in a fluid medium(the fluid-plate system)is obtained.The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass.The GalerkinVlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium.The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature.The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail.These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium.Thereby,they offer appropriate operational approaches for the structure when employed in various mediums.

Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink

With its complex nonlinear dynamic behavior,the tristable system has shown excellent performance in areas such as energy harvesting and vibration suppression,and has attracted a lot of attention.In this paper,an asymmetric tristable design is proposed to improve the vibration suppression efficiency of nonlinear energy sinks(NESs)for the first time.The proposed asymmetric tristable NES(ATNES)is composed of a pair of oblique springs and a vertical spring.Then,the three stable states,symmetric and asymmetric,can be achieved by the adjustment of the distance and stiffness asymmetry of the oblique springs.The governing equations of a linear oscillator(LO)coupled with the ATNES are derived.The approximate analytical solution to the coupled system is obtained by the harmonic balance method(HBM)and verified numerically.The vibration suppression efficiency of three types of ATNES is compared.The results show that the asymmetric design can improve the efficiency of vibration reduction through comparing the chaotic motion of the NES oscillator between asymmetric steady states.In addition,compared with the symmetrical tristable NES(TNES),the ATNES can effectively control smaller structural vibrations.In other words,the ATNES can effectively solve the threshold problem of TNES failure to weak excitation.Therefore,this paper reveals the vibration reduction mechanism of the ATNES,and provides a pathway to expand the effective excitation amplitude range of the NES.

Snap-through behaviors and nonlinear vibrations of a bistable composite laminated cantilever shell:an experimental and numerical study

The snap-through behaviors and nonlinear vibrations are investigated for a bistable composite laminated cantilever shell subjected to transversal foundation excitation based on experimental and theoretical approaches.An improved experimental specimen is designed in order to satisfy the cantilever support boundary condition,which is composed of an asymmetric region and a symmetric region.The symmetric region of the experimental specimen is entirely clamped,which is rigidly connected to an electromagnetic shaker,while the asymmetric region remains free of constraint.Different motion paths are realized for the bistable cantilever shell by changing the input signal levels of the electromagnetic shaker,and the displacement responses of the shell are collected by the laser displacement sensors.The numerical simulation is conducted based on the established theoretical model of the bistable composite laminated cantilever shell,and an off-axis three-dimensional dynamic snap-through domain is obtained.The numerical solutions are in good agreement with the experimental results.The nonlinear stiffness characteristics,dynamic snap-through domain,and chaos and bifurcation behaviors of the shell are quantitatively analyzed.Due to the asymmetry of the boundary condition and the shell,the upper stable-state of the shell exhibits an obvious soft spring stiffness characteristic,and the lower stable-state shows a linear stiffness characteristic of the shell.

Nonlinear phenomena in vibrations of embedded carbon nanotubes conveying viscous fluid

Various nonlinear phenomena such as bifurcations and chaos in the responses of carbon nanotubes(CNTs)are recognized as being major contributors to the inaccuracy and instability of nanoscale mechanical systems.Therefore,the main purpose of this paper is to predict the nonlinear dynamic behavior of a CNT conveying viscousfluid and supported on a nonlinear elastic foundation.The proposed model is based on nonlocal Euler–Bernoulli beam theory.The Galerkin method and perturbation analysis are used to discretize the partial differential equation of motion and obtain the frequency-response equation,respectively.A detailed parametric study is reported into how the nonlocal parameter,foundation coefficients,fluid viscosity,and amplitude and frequency of the external force influence the nonlinear dynamics of the system.Subharmonic,quasi-periodic,and chaotic behaviors and hardening nonlinearity are revealed by means of the vibration time histories,frequency-response curves,bifurcation diagrams,phase portraits,power spectra,and Poincarémaps.Also,the results show that it is possible to eliminate irregular motion in the whole range of external force amplitude by selecting appropriate parameters.

Nonlinear metamaterial enabled aeroelastic vibration reduction of a supersonic cantilever wing plate

The violent vibration of supersonic wings threatens aircraft safety.This paper proposes the strongly nonlinear acoustic metamaterial(NAM)method to mitigate aeroelastic vibration in supersonic wing plates.We employ the cantilever plate to simulate the practical behavior of a wing.An aeroelastic vibration model of the NAM cantilever plate is established based on the mode superposition method and a modified third-order piston theory.The aerodynamic properties are systematically studied using both the timedomain integration and frequency-domain harmonic balance methods.While presenting the flutter and post-flutter behaviors of the NAM wing,we emphasize more on the preflutter broadband vibration that is prevalent in aircraft.The results show that the NAM method can reduce the low-frequency and broadband pre-flutter steady vibration by 50%-90%,while the post-flutter vibration is reduced by over 95%,and the critical flutter velocity is also slightly delayed.As clarified,the significant reduction arises from the bandgap,chaotic band,and nonlinear resonances of the NAM plate.The reduction effect is robust across a broad range of parameters,with optimal performance achieved with only 10%attached mass.This work offers a novel approach for reducing aeroelastic vibration in aircraft,and it expands the study of nonlinear acoustic/elastic metamaterials.

A vibration isolator with a controllable quasi-zero stiffness region based on nonlinear force design

To achieve stability optimization in low-frequency vibration control for precision instruments,this paper presents a quasi-zero stiffness(QZS)vibration isolator with adjustable nonlinear stiffness.Additionally,the stress-magnetism coupling model is established through meticulous theoretical derivation.The controllable QZS interval is constructed via parameter design and magnetic control,effectively segregating the high static stiffness bearing section from the QZS vibration isolation section.Furthermore,a displacement control scheme utilizing a magnetic force is proposed to regulate entry into the QZS working range for the vibration isolation platform.Experimental results demonstrate that the operation within this QZS region reduces the peak-to-peak acceleration signal by approximately 66.7%compared with the operation outside this region,thereby significantly improving the low frequency performance of the QZS vibration isolator.

Nonlinear Flap-Wise Vibration Characteristics ofWind Turbine Blades Based onMulti-Scale AnalysisMethod

This work presents a novel approach to achieve nonlinear vibration response based on the Hamilton principle.We chose the 5-MW reference wind turbine which was established by the National Renewable Energy Laboratory(NREL),to research the effects of the nonlinear flap-wise vibration characteristics.The turbine wheel is simplified by treating the blade of a wind turbine as an Euler-Bernoulli beam,and the nonlinear flap-wise vibration characteristics of the wind turbine blades are discussed based on the simplification first.Then,the blade’s large-deflection flap-wise vibration governing equation is established by considering the nonlinear term involving the centrifugal force.Lastly,it is truncated by the Galerkin method and analyzed semi-analytically using the multi-scale analysis method,and numerical simulations are carried out to compare the simulation results of finite elements with the numerical simulation results using Campbell diagram analysis of blade vibration.The results indicated that the rotational speed of the impeller has a significant impact on blade vibration.When the wheel speed of 12.1 rpm and excitation amplitude of 1.23 the maximum displacement amplitude of the blade has increased from 0.72 to 3.16.From the amplitude-frequency curve,it can be seen that the multi-peak characteristic of blade amplitude frequency is under centrifugal nonlinearity.Closed phase trajectories in blade nonlinear vibration,exhibiting periodic motion characteristics,are found through phase diagrams and Poincare section diagrams.

Research on the Damping Mechanism of Time-Delay Coupled Negative Stiffness Dynamic Absorber in Nonlinear Vibration Damping System

A study was conducted on the effect of time delay and structural parameters on the vibration reduction of a time delayed coupled negative stiffness dynamic absorber in nonlinear vibration reduction systems. Taking dynamic absorbers with different structural and control parameters as examples, the effects of third-order nonlinear coefficients, time-delay control parameters, and negative stiffness coefficients on reducing the replication of the main system were discussed. The nonlinear dynamic absorber has a very good vibration reduction effect at the resonance point of the main system and a nearby area, and when 1 increases to a certain level, the stable region of the system continues to increase. The amplitude curve of the main system of a nonlinear dynamic absorber will generate Hop bifurcation and saddle node bifurcation in the region far from the resonance point, resulting in almost periodic motion and jumping phenomena in the system. For nonlinear dynamic absorbers with determined structural parameters, time-delay feedback control can be adopted to control the amplitude of the main system. For different negative stiffness coefficients, there exists a minimum damping point for the amplitude of the main system under the determined system structural parameters and time-delay feedback control parameters.

A viscoelastic metamaterial beam for integrated vibration isolation and energy harvesting

Locally resonant metamaterials have low-frequency band gaps and the capability of converging vibratory energy in the band gaps at resonant cells.It has been demonstrated by several researchers that the dissipatioin of vibratory energy within the band gap can be improved by using viscoelastic materials.This paper designs an integrated viscoelastic metamaterial for energy harvesting and vibration isolation.The viscoelastic metamaterial is achieved by a viscoelastic beam periodically arrayed with spatial ball-pendulum nonlinear energy harvesters.The nonlinear resonator with an energy harvesting function is achieved by placing a free-rolling magnetic ball in a spherical cavity with an additional induction coil.The dynamic equations of viscoelastic metamaterials under transverse excitation are established,and the energy harvesting and vibration isolation characteristics within the dispersion relation of viscoelastic metamaterials are analyzed.The results show that the vibrations of the main body of the viscoelastic metamaterial beam are significantly suppressed in the frequency range of the local resonance band gap.At the same time,the elastic waves are limited in the nonlinear resonator with an energy harvesting function,which improves the energy output.Finally,an experimental platform of viscoelastic metamaterial vibration is established for validation purposes.

Dynamic analysis of a novel multilink-spring mechanism for vibration isolation and energy harvesting

Due to technical limitations,existing vibration isolation and energy harvesting(VIEH)devices have poor performance at low frequency.This paper proposes a new multilink-spring mechanism(MLSM)that can be used to solve this problem.The VIEH performance of the MLSM under harmonic excitation and Gaussian white noise was analyzed.It was found that the MLSM has good vibration isolation performance for low-frequency isolation and the frequency band can be widened by adjusting parameters to achieve a higher energy harvesting power.By comparison with two special cases,the results show that the MLSM is basically the same as the other two oscillators in terms of vibration isolation but has better energy harvesting performance under multistable characteristics.The MLSM is expected to reduce the impact of vibration on high-precision sensitive equipment in some special sites such as subways and mines,and at the same time supply power to structural health monitoring devices.

Theoretical and experimental investigations on an X-shaped vibration isolator with active controlled variable stiffness

A novel X-shaped variable stiffness vibration isolator(X-VSVI)is proposed.The Runge-Kutta method,harmonic balance method,and wavelet transform spectra are introduced to evaluate the performance of the X-VSVI under various excitations.The layer number,the installation angle of the X-shaped structure,the stiffness,and the active control parameters are systematically analyzed.In addition,a prototype of the X-VSVI is manufactured,and vibration tests are carried out.The results show that the proposed X-VSVI has a superior adaptability to that of a traditional X-shaped mechanism,and shows excellent vibration isolation performance in response to different amplitudes and forms of excitations.Moreover,the vibration isolation efficiency of the device can be improved by appropriate adjustment of parameters.

Nonreciprocity of energy transfer in a nonlinear asymmetric oscillator system with various vibration states

The nonreciprocity of energy transfer is constructed in a nonlinear asymmetric oscillator system that comprises two nonlinear oscillators with different parameters placed between two identical linear oscillators.The slow-flow equation of the system is derived by the complexification-averaging method.The semi-analytical solutions to this equation are obtained by the least squares method,which are compared with the numerical solutions obtained by the Runge-Kutta method.The distribution of the average energy in the system is studied under periodic and chaotic vibration states,and the energy transfer along two opposite directions is compared.The effect of the excitation amplitude on the nonreciprocity of the system producing the periodic responses is analyzed,where a three-stage energy transfer phenomenon is observed.In the first stage,the energy transfer along the two opposite directions is approximately equal,whereas in the second stage,the asymmetric energy transfer is observed.The energy transfer is also asymmetric in the third stage,but the direction is reversed compared with the second stage.Moreover,the excitation amplitude for exciting the bifurcation also shows an asymmetric characteristic.Chaotic vibrations are generated around the resonant frequency,irrespective of which linear oscillator is excited.The excitation threshold of these chaotic vibrations is dependent on the linear oscillator that is being excited.In addition,the difference between the energy transfer in the two opposite directions is used to further analyze the nonreciprocity in the system.The results show that the nonreciprocity significantly depends on the excitation frequency and the excitation amplitude.

Nonlinear free vibration of piezoelectric semiconductor doubly-curved shells based on nonlinear drift-diffusion model

In this paper, the nonlinear free vibration behaviors of the piezoelectric semiconductor(PS) doubly-curved shell resting on the Pasternak foundation are studied within the framework of the nonlinear drift-diffusion(NLDD) model and the first-order shear deformation theory. The nonlinear constitutive relations are presented, and the strain energy, kinetic energy, and virtual work of the PS doubly-curved shell are derived.Based on Hamilton's principle as well as the condition of charge continuity, the nonlinear governing equations are achieved, and then these equations are solved by means of an efficient iteration method. Several numerical examples are given to show the effect of the nonlinear drift current, elastic foundation parameters as well as geometric parameters on the nonlinear vibration frequency, and the damping characteristic of the PS doublycurved shell. The main innovations of the manuscript are that the difference between the linearized drift-diffusion(LDD) model and the NLDD model is revealed, and an effective method is proposed to select a proper initial electron concentration for the LDD model.

Nonlinear vibrations of a composite circular plate with a rigid body

The influence of weights is usually ignored in the study of nonlinear vibrations of plates.In this paper,the effect of structure weights on the nonlinear vibration of a composite circular plate with a rigid body is presented.The nonlinear governing equations are derived from the generalized Hamilton's principle and the von Kármán plate theory.The equilibrium configurations due to weights are determined and validated by the finite element method(FEM).A nonlinear model for the vibration around the equilibrium configuration is established.Moreover,the natural frequencies and amplitude-frequency responses of harmonically forced vibrations are calculated.The study shows that the structure weights introduce additional linear and quadratic nonlinear terms into the dynamical model.This leads to interesting phenomena.For example,considering weights increases the natural frequency.Furthermore,when the influence of weights is considered,the vibration response of the plate becomes asymmetrical.

Vertical vibration control using nonlinear energy sink with inertial amplifier

To reduce additional mass, this work proposes a nonlinear energy sink(NES)with an inertial amplifier(NES-IA) to control the vertical vibration of the objects under harmonic and shock excitations. Moreover, this paper constructs pure nonlinear stiffness without neglecting the gravity effect of the oscillator. Both analytical and numerical methods are used to evaluate the performance of the NES-IA. The research findings indicate that even if the actual mass is 1% of the main oscillator, the NES-IA with proper inertia angles and mass distribution ratios can still effectively attenuate the steady-state and transient responses of the main oscillator. Nonlinear stiffness and damping also have important effects. Due to strongly nonlinear factors, the coupled system may exhibit higher branch responses under harmonic excitation. In shock excitation environment, the NES-IA with a large dynamic mass can trigger energy capture of both main resonance and high-frequency resonance. Furthermore, the comparison with the traditional NES also confirms the advantages of the NES-IA in overcoming mass dependence.

Stabilities Analysis of Electromechanical Nonlinear Vibration of Electric Machine

An electromechanical nonlinear model of rotor system of electric machine is built.Respondance curves in parameter excited nonlinear vibration of this system caused by electromagnetic forces are investigated.Further more,the analysis reveals the effects of various electromagnetic and mechanical parameters on resonances, and some valuable results are obtained.The analytical result of this paper provides electric machine with the condition of 1/2 subharmonic resonance under the electromechanical electromagnetic forces.Electromagnetic forces apparently affect the stability zone, and both linear term and nonlinear term can excite parametric resonance.The revealed dynamic phenomena provide some new theories and active methods for the fault recognition of electric machine and the defination of stability range,and the theoretical bases for qualitatively controlling the stable operating state of rotors.

Vibration control of fluid-conveying pipes: a state-of-the-art review

Fluid-conveying pipes are widely used to transfer bulk fluids from one point to another in many engineering applications.They are subject to various excitations from the conveying fluids,the supporting structures,and the working environment,and thus are prone to vibrations such as flow-induced vibrations and acoustic-induced vibrations.Vibrations can generate variable dynamic stress and large deformation on fluid-conveying pipes,leading to vibration-induced fatigue and damage on the pipes,or even leading to failure of the entire piping system and catastrophic accidents.Therefore,the vibration control of fluid-conveying pipes is essential to ensure the integrity and safety of pipeline systems,and has attracted considerable attention from both researchers and engineers.The present paper aims to provide an extensive review of the state-of-the-art research on the vibration control of fluid-conveying pipes.The vibration analysis of fluid-conveying pipes is briefly discussed to show some key issues involved in the vibration analysis.Then,the research progress on the vibration control of fluid-conveying pipes is reviewed from four aspects in terms of passive control,active vibration control,semi-active vibration control,and structural optimization design for vibration reduction.Furthermore,the main results of existing research on the vibration control of fluid-conveying pipes are summarized,and future promising research directions are recommended to address the current research gaps.This paper contributes to the understanding of vibration control of fluid-conveying pipes,and will help the research work on the vibration control of fluidconveying pipes attract more attention.

A bio-inspired spider-like structure isolator for low-frequency vibration

This paper proposes a quasi-zero stiffness(QZS)isolator composed of a curved beam(as spider foot)and a linear spring(as spider muscle)inspired by the precise capturing ability of spiders in vibrating environments.The curved beam is simplified as an inclined horizontal spring,and a static analysis is carried out to explore the effects of different structural parameters on the stiffness performance of the QZS isolator.The finite element simulation analysis verifies that the QZS isolator can significantly reduce the first-order natural frequency under the load in the QZS region.The harmonic balance method(HBM)is used to explore the effects of the excitation amplitude,damping ratio,and stiffness coefficient on the system’s amplitude-frequency response and transmissibility performance,and the accuracy of the analytical results is verified by the fourth-order Runge-Kutta integral method(RK-4).The experimental data of the QZS isolator prototype are fitted to a ninth-degree polynomial,and the RK-4 can theoretically predict the experimental results.The experimental results show that the QZS isolator has a lower initial isolation frequency and a wider isolation frequency bandwidth than the equivalent linear isolator.The frequency sweep test of prototypes with different harmonic excitation amplitudes shows that the initial isolation frequency of the QZS isolator is 3 Hz,and it can isolate 90%of the excitation signal at 7 Hz.The proposed biomimetic spider-like QZS isolator has high application prospects and can provide a reference for optimizing low-frequency or ultra-low-frequency isolators.

Integrated device for multiscale series vibration reduction and energy harvesting

A multi-degree-of-freedom device is proposed,which can achieve efficient vibration reduction as the main objective and energy harvesting as the secondary purpose.The device comprises a multiscale nonlinear vibration absorber(NVA)and piezoelectric components.Energy conversion and energy measurement methods are used to evaluate the device performance from multiple perspectives.Research has shown that this device can efficiently transfer transient energy from the main structure and convert a portion of transient energy into electrical energy.Main resonance and higher-order resonance are the main reasons for efficient energy transfer.The device can maintain high vibration reduction performance even when the excitation amplitude changes over a large range.Compared with the single structures with and without precompression,the multiscale NVA-piezoelectric device offers significant vibration reduction advantages.In addition,there are significant differences in the parameter settings of the two substructures for vibration reduction and energy harvesting.

Global Dynamic Characteristic of Nonlinear Torsional Vibration System under Harmonically Excitation

Torsional vibration generally causes serious instability and damage problems in many rotating machinery parts. The global dynamic characteristic of nonlinear torsional vibration system with nonlinear rigidity and nonlinear friction force is investigated. On the basis of the generalized dissipation Lagrange＇s equation, the dynamics equation of nonlinear torsional vibration system is deduced. The bifurcation and chaotic motion in the system subjected to an external harmonic excitation is studied by theoretical analysis and numerical simulation. The stability of unperturbed system is analyzed by using the stability theory of equilibrium positions of Hamiltonian systems. The criterion of existence of chaos phenomena under a periodic perturbation is given by means of Melnikov＇s method. It is shown that the existence of homoclinic and heteroclinic orbits in the unperturbed system implies chaos arising from breaking of homoclinic or heteroclinic orbits under perturbation. The validity of the result is checked numerically. Periodic doubling bifurcation route to chaos, quasi-periodic route to chaos, intermittency route to chaos are found to occur due to the amplitude varying in some range. The evolution of system dynamic responses is demonstrated in detail by Poincare maps and bifurcation diagrams when the system undergoes a sequence of periodic doubling or quasi-periodic bifurcations to chaos. The conclusion can provide reference for deeply researching the dynamic behavior of mechanical drive systems.