A low-frequency and broadband wave-insulating vibration isolator based on plate-shaped metastructures

A metamaterial vibration isolator,termed as wave-insulating isolator,is proposed,which preserves enough load-bearing capability and offers ultra-low and broad bandgaps for greatly enhanced wave insulation.It consists of plate-shaped metacells,whose symmetric and antisymmetric local resonant modes offer several low and broad mode bandgaps although the complete bandgap remains high and narrow.The bandgap mechanisms,vibration isolation properties,effects of key parameters,and robustness to complex conditions are clarified.As experimentally demonstrated,the wave-insulating isolator can improve the vibration insulation in the ranges of[50 Hz,180 Hz]and[260 Hz,400 Hz]by 15 dB and 25 dB,respectively,in contrast to the conventional isolator with the same first resonant frequency.

Application and optimization design of non-obstructive particle damping-phononic crystal vibration isolator in viaduct structure-borne noise reduction

The problems associated with vibrations of viaducts and low-frequency structural noise radiation caused by train excitation continue to increase in importance.A new floating-slab track vibration isolator-non-obstructive particle damping-phononic crystal vibration isolator is proposed herein,which uses the particle damping vibration absorption technology and bandgap vibration control theory.The vibration reduction performance of the NOPD-PCVI was analyzed from the perspective of vibration control.The paper explores the structure-borne noise reduction performance of the NOPD-PCVIs installed on different bridge structures under varying service conditions encountered in practical engineering applications.The load transferred to the bridge is obtained from a coupled train-FST-bridge analytical model considering the different structural parameters of bridges.The vibration responses are obtained using the finite element method,while the structural noise radiation is simulated using the frequency-domain boundary element method.Using the particle swarm optimization algorithm,the parameters of the NOPD-PCVI are optimized so that its frequency bandgap matches the dominant bridge structural noise frequency range.The noise reduction performance of the NOPD-PCVIs is compared to the steel-spring isolation under different service conditions.

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.

A human-sensitive frequency band vibration isolator for heavy-duty truck seats

In this study,a human-sensitive frequency band vibration isolator(HFBVI)with quasi-zero stiffness(QZS)characteristics for heavy-duty truck seats is designed to improve the comfort of heavy-duty truck drivers on uneven roads.First,the analytical expressions for the force and displacement of the HFBVI are derived with the Lagrange equation and d'Alembert's principle,and are validated through the prototype restoring force testing.Second,the harmonic balance method(HBM)is used to obtain the dynamic responses under harmonic excitation,and further the influence of pre-stretching on the dynamic characteristics and transmissibility is discussed.Finally,the experimental prototype of the HFBVI is fabricated,and vibration experiments are conducted under harmonic excitation to verify the vibration isolation performance(VIP)of the proposed vibration isolator.The experimental results indicate that the HFBVI can effectively suppress the frequency band(4-8 Hz)to which the human body is sensitive to vertical vibration.In addition,under real random road spectrum excitation,the HFBVI can achieve low-frequency vibration isolation close to 2 Hz,providing new prospects for ensuring the health of heavy-duty truck drivers.

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.

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.

Multi-layer quasi-zero-stiffness meta-structure for high-efficiency vibration isolation at low frequency

An easily stackable multi-layer quasi-zero-stiffness(ML-QZS)meta-structure is proposed to achieve highly efficient vibration isolation performance at low frequency.First,the distributed shape optimization method is used to design the unit cel,i.e.,the single-layer QZS(SL-QZS)meta-structure.Second,the stiffness feature of the unit cell is investigated and verified through static experiments.Third,the unit cells are stacked one by one along the direction of vibration isolation,and thus the ML-QZS meta-structure is constructed.Fourth,the dynamic modeling of the ML-QZS vibration isolation metastructure is conducted,and the dynamic responses are obtained from the equations of motion,and verified by finite element(FE)simulations.Finally,a prototype of the ML-QZS vibration isolation meta-structure is fabricated by additive manufacturing,and the vibration isolation performance is evaluated experimentally.The results show that the vibration isolation performance substantially enhances when the number of unit cells increases.More importantly,the ML-QZS meta-structure can be easily extended in the direction of vibration isolation when the unit cells are properly stacked.Hence,the ML-FQZS vibration isolation meta-structure should be a fascinating solution for highly efficient vibration isolation performance at low frequency.

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.

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.

Mechanical properties of disc-spring vibration isolators based on boundary friction

To ascertain the influence of the boundary friction on mechanical properties of disc-spring vibration isolators a load-displacement hysteresis curve formula of disc-spring vibration isolators is derived on the basis of the energy conservation law as well as considering the effect of the boundary friction.The formula is validated through the finite element analysis and static load tests.On this basis the effect of the boundary friction on the bearing capacity is researched. Then the dynamic performance of disc-spring vibration isolators is studied by dynamic tests.The experimental results indicate that the boundary friction can promise a larger damping with a ratio of 0.23 for disc-spring vibration isolators.Compared with the loading frequency the loading amplitude has a greater impact on the energy consumption dynamic stiffness and damping of vibration isolators.This research can provide valuable information for the design of disc-spring vibration isolators.

Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine

Human motion induced vibration has very low frequency,ranging from 2 Hz to 5 Hz.Traditional vibration isolators are not effective in low-frequency regions due to the trade-off between the low natural frequency and the high load capacity.In this paper,inspired by the human spine,we propose a novel bionic human spine inspired quasi-zero stiffness(QZS)vibration isolator which consists of a cascaded multi-stage negative stiffness structure.The force and stiffness characteristics are investigated first,the dynamic model is established by Newton’s second law,and the isolation performance is analyzed by the harmonic balance method(HBM).Numerical results show that the bionic isolator can obtain better low-frequency isolation performance by increasing the number of negative structure stages,and reducing the damping values and external force values can obtain better low-frequency isolation performance.In comparison with the linear structure and existing traditional QZS isolator,the bionic spine isolator has better vibration isolation performance in low-frequency regions.It paves the way for the design of bionic ultra-low-frequency isolators and shows potential in many engineering applications.

Using a SVM to evaluate damage to vibration isolators in an elastic raft system

Predicting damage to vibration isolators in a raft experiencing heavy shock loadings from explosions is an important task when designing a raft system. It is also vital to be able to research the vulnerability of heavily shocked floating rafts unreliable, especially when the allowable values The conventional approach to prediction has been or ultimate values of vibration isolators of supposedly uniform standard in a raft actually have differing and uncertain values due to defective workmanship. A new model for predicting damage to vibration isolators in a shocked floating raft system is presented in this paper. It is based on a support vector machine（SVM）, which uses Artificial Intelligence to characterize complicated nonlinear mapping between the impacting environment and damage to the vibration isolators. The effectiveness of the new method for predicting damage was illustrated by numerical simulations, and shown to be effective when relevant parameters of the model were chosen reasonably. The effect determining parameters, including kernel function and penalty factors, has on prediction results is also discussed. It can be concluded that the SVM will probably become a valid tool to study damage or vulnerability in a shocked raft system.

Design and Analysis of a Horizontal Quasi-Zero Stiffness Vibration Isolator by Combining Rolling-Ball and Disk Springs in Parallel

Combining disk springs having negative stiffness with a rolling-ball in parallel is proposed in this paper. It is used to reduce the system stiffness and the positioning error in a non-ideal environment.The characteristics of a disk spring are analyzed. The dynamic equation of its motion has been obtained based on Newton＇s second law. After definition of a error margin,the dynamic equation of the motion can be treated as a Duffing oscillator,and the influences of non-dimensional parameters on the stiffness and transmissibility are studied. The natural frequency and transmissibility are achieved in a linearization range,where the ratio of linear to nonlinear items is small enough.The influence of mass ratio and non-dimensional parameters on natural frequency are analyzed. Finally,a comparison of numerical example demonstrates that the QZS system can realize a lower stiffness within an increased range.

Dynamics of installation way for the actuator of a two-stage active vibration-isolator

We investigated the behaviors of an active control system of two-stage vibration isolation with the actuator installed in parallel with either the upper passive mount or the lower passive isolation mount. We revealed the relationships between the active control force of the actuator and the parameters of the passive isolators by studying the dynamics of two-stage active vibration isolation for the actuator at the foregoing two positions in turn. With the actuator installed beside the upper mount, a small active force can achieve a very good isolating effect when the frequency of the stimulating force is much larger than the natural frequency of the upper mount; a larger active force is required in the low-frequency domain; and the active force equals the stimulating force when the upper mount works within the resonance region, suggesting an approach to reducing wobble and ensuring desirable installation accuracy by increasing the upper-mount stiffness. In either the low or the high frequency region far away from the resonance region, the active force is smaller when the actuator is beside the lower mount than beside the upper mount.

DOUBLE LOOP ACTIVE VIBRATION CONTROL OF PNEUMATIC ISOLATOR WITH TWO SEPARATE CHAMBERS

A newly designed pneumatic spring with two separate chambers is promoted and double-loop active control is introduced to overcome the following drawbacks of passive pneumatic isolation： ① The low frequency resonances introduced into the system; ② Conflict between lower isolation frequency and stiffness high enough to limit quasi-static stroke;③ Inconsistent isolation level with different force load. The design of two separate chambers is for the purpose of tuning support frequency and force independently and each chamber is controlled by a different valve. The inner one of double-loop structure is pressure control, and in order to obtain good performance, nonlinearities compensation and motion flow rate compensation （MFRC） are added besides the basic cascade compensation, and the influence of tube length is studied. The outer loop has two functions： one is to eliminate the resonance caused by isolation support and to broaden the isolation frequency band by payload velocity feedback and base velocity feed forward, and the other is to tune support force and support stiffness simultaneously and independently, which means the support force will have no effect on support stiffness. Theoretical analysis and experiment results show that the three drawbacks are overcome simultaneously.

A Closed-Loop Dynamic Controller for Active Vibration Isolation Working on A Parallel Wheel-Legged Robot

Serving the Stewart mechanism as a wheel-legged structure,the most outstanding superiority of the proposed wheel-legged hybrid robot(WLHR)is the active vibration isolation function during rolling on rugged terrain.However,it is difficult to obtain its precise dynamic model,because of the nonlinearity and uncertainty of the heavy robot.This paper presents a dynamic control framework with a decentralized structure for single wheel-leg,position tracking based on model predictive control(MPC)and adaptive impedance module from inside to outside.Through the Newton-Euler dynamic model of the Stewart mechanism,the controller first creates a predictive model by combining Newton-Raphson iteration of forward kinematic and inverse kinematic calculation of Stewart.The actuating force naturally enables each strut to stretch and retract,thereby realizing six degrees-of-freedom(6-DOFs)position-tracking for Stewart wheel-leg.The adaptive impedance control in the outermost loop adjusts environmental impedance parameters by current position and force feedback of wheel-leg along Z-axis.This adjustment allows the robot to adequately control the desired support force tracking,isolating the robot body from vibration that is generated from unknown terrain.The availability of the proposed control methodology on a physical prototype is demonstrated by tracking a Bezier curve and active vibration isolation while the robot is rolling on decelerate strips.By comparing the proportional and integral(PI)and constant impedance controllers,better performance of the proposed algorithm was operated and evaluated through displacement and force sensors internally-installed in each cylinder,as well as an inertial measurement unit(IMU)mounted on the robot body.The proposed algorithm structure significantly enhances the control accuracy and vibration isolation capacity of parallel wheel-legged robot.

Material Model Research on Rubber Vibration Isolators

A viscohyperelastic constitutive model is proposed to describe the mechanical behaviour of vibration isolation rubber under broad-band vibration. This constitutive model comprises two parts： a component with three parameters to characterize the hyperelastic static properties of rubber materials, and the other component incorporating two relaxation time parameters, corresponding to high and low strain rates, respectively, to describe the dynamic response under vibration and impact loadings. Based on this proposed constitutive model, a series of experiments were performed on two types of rubber materials over a wide strain rate range. The results predicted from this model are in good agreement with the experimental data.

Effects of Fatigue Characteristics on Static and Dynamic Performance of Eucommia Rubber Isolators

This study aimed to investigate the effect of fatigue characteristics on the static and dynamic performance of Eucommia ulmoides gum isolators, and to explore the performance changes of Eucommia ulmoides gum isolators with different formulations. For this purpose, we used five formulations of Eucommia ulmoides gum isolators and set different fatigue test methods to study the static and dynamic performance changes of Eucommia ulmoides gum isolators with different formulations by changing the amplitude. The experimental results showed that the addition of Eucommia ulmoides gum had an impact on the performance of the isolator, and the number of fatigue cycles would lead to the hardening of the Eucommia ulmoides gum isolator and changes in its static and dynamic performance. In the range of two million vibrations, the performance change of the isolator was significant in the early stage and then tended to be flat, indicating that the impact of fatigue on the performance of the isolator would not continue to persist. It is worth noting that the study found that the addition of 30% Eucommia ulmoides gum had the least impact on the performance of the isolator under fatigue. Therefore, for long-term use of Eucommia ulmoides gum isolators, attention should be paid to their fatigue characteristics to ensure their stability and reliability. Additionally, this study provides a reference for the design and application of Eucommia ulmoides gum isolators. In summary, this study provides important reference value for a deeper understanding of the fatigue characteristics of Eucommia ulmoides gum isolators and for ensuring their stable and reliable performance. .

Vibration Isolation Characteristics of Impedance-balanced Ship Equipment Foundation under Unbalanced Excitation

A new type of impedance-balanced ship equipment foundation structure based on the principle of impedance balancing using a“discontinuous panel-vibration isolation liquid layer-foundation structure”is proposed to solve the problem of poor low-frequency vibration isolation of the foundation under unbalanced excitation of shipboard equipment.Based on the finite element method,the influence of characteristic parameters of the foundation panel structure on its vibration reduction characteristics under unbalanced excitation is explored.The results show that the vibration isolation level of the impedance-balanced foundation is 10 dB higher than the traditional foundation in the low-frequency band of 10-500 Hz when subjected to combined excitation of concentrated force and moment.Increasing the thickness of the impedance-balanced foundation panel can enhance the isolation effect.Increasing the number of sub-panels can effectively reduce the vibration response of the foundation panel and enhance the isolation performance of the foundation.The connection stiffness between sub-panels has a small effect on the isolation performance of the foundation.

Multi Objective Robust Active Vibration Control for Flexure Jointed Struts of Stewart Platforms via H∞ and μ Synthesis

Active vibration control is needed for future space telescopes, space laser communication and other precision sensitive payloads which require ultra-quiet environments. A Stewart platform based hybrid isolator with 6 hybrid struts is the effective system for active/passive vibration isolation over 5-250 Hz band. Using an identification transfer matrix of the Stewart platform, the coupling analysis of six channels is provided. A dynamics model is derived, and the rigid mode is removed to keep the signal of pointing control. Multi objective robust H∞ and μ synthesis strategies, based on singular values and structured singular values respectively, are presented, which simultaneously satisfy the low frequency pointing and high frequency disturbance rejection requirements and take account of the model uncertainty, parametric uncertainty and sensor noise. Then, by performing robust stability test, it is shown that the two controllers are robust to the uncertainties, the robust stability margin of H, controller is less than that of μ controller, but the order of μ controller is higher than that of H, controller, so the balanced controller reduction is provided. Additionally, the μ controller is compared with a PI controller. The time domain simulation of the μ controller indicates that the two robust control strategies are effective for keeping the pointing command and isolating the harmonic and stochastic disturbances.