Nonlinear Vibration Isolation Research Articles

Research on flexible beam-type nonlinear vibration isolators suitable for low frequencies

Ship vibration not only causes safety issues, but also easily generates noise pollution. Therefore, this paper introduces the quasi-zero stiffness (QZS) vibration isolator to solve the problem of low-frequency vibration. In terms of static analysis, this paper proposes a discretized beam constraint model (DBCM) to study the static properties of flexible beams with large deformation, and the finite element analysis (FEA) verifies the accuracy of DBCM. Regarding dynamic analysis, this paper combines the harmonic balance method (HBM) and the pseudo-arc length method (PALM) to analyze the dynamic response and explore the influence of excitation and damping ratio on the response stability. In addition, the performance of equivalent linear isolators is compared, revealing significant advantages of QZS isolator in terms of isolation bandwidth and peak transmissibility. The experimental data demonstrates that QZS isolator’s initial isolation frequency (2.14 Hz) is 68.5% lower than that of linear isolators (6.79 Hz), and the isolation efficiency at 5.35 Hz can reach 90%, making it suitable for low-frequency isolation. Furthermore, experimental data validate the accuracy of the theoretical model and FEA. The static and dynamic theoretical models can optimize the structural parameters of flexible beams and serve as valuable inspiration and reference for designing and improving isolator.

Study on vibration response and isolation of substation structure under subway load excitation

This study takes the indoor substation adjacent to the elevated bridge subway line as the engineering background, investigates the structural vibration response law of the substation induced by the operation of the subway line through on-site vibration measurement, and proposes a novel nonlinear gas-spring quasi-zero stiffness isolator (NGS-QZSI) is proposed to reduce the structural vertical vibration and further reduce the safety distance. The software ABAQUS is used to establish a structure-equipment coupling numerical analysis model considering soil-structure interaction, and its effectiveness and accuracy are validated based on the measured results. The structural vibration response analysis is carried out under different vibration source distances, and a nonlinear gas-spring quasi-zero stiffness isolator is proposed to be employed for substation structural vibration isolation. The research results show that the substation structure under subway load excitation is dominated by vertical vibration, and its vibration response increases gradually with the increase of floor level. When the substation structure is less than 45 m from the subway line, the structural response exceeds the safety limit (12.5 μm/s) of the VC-C standard. With the vibration isolator attached, the structural vibration response is significantly reduced, with the peak and root mean square response controlled by more than 70 %. Particularly, the safe distance of the substation from the subway line is reduced from 45 m to 20 m. Moreover, the frequency domain result analysis indicates that the proposed nonlinear vibration isolator can effectively control the low-frequency vibration of the structure.

Nonlinear behavior of quasi-zero stiffness nonlinear torsional vibration isolator

Nonlinear behavior of quasi-zero stiffness nonlinear torsional vibration isolator

Analytical study on nonlinear frequency response and vibration isolation of multistage clutch damper in automotive powertrain

This paper studies the nonlinear frequency response and vibration isolation performance of the multistage clutch damper at resonance. First, a 2-DOF drivetrain model is established considering the piecewise-linear stiffness, piecewise-linear damping and asymmetric transition angles of the multistage clutch damper. Then, the averaging method is employed to deduce the analytical solution of the nonlinear motion equation, and the stability of the periodic solution is studied using Routh-Hurwitz criterion. The nonlinear behaviors of the oscillator are discussed based on the theoretical results, and the numerical simulation is carried out to verify the credibility of the proposed method. Finally, the sensitivity analysis is conducted to investigate the influence of the system parameters on the amplitude-frequency response of the multistage clutch damper. The results indicate that the isolation performance of the multistage clutch damper is sensitive to the first and second stages of damping and the first-stage transition angles. By increasing the first and second stages of viscous damping by 50% and simultaneously reducing the first-stage angle range by 3° with 1° asymmetry, the isolation performance of the clutch damper is effectively improved, reducing the vibration amplitude at resonance by 28.8%.

Theoretical and experimental study of a novel nonlinear quasi-zero Stiffness vibration isolator based on a symmetric link-rod-type structure

This study proposes a novel nonlinear low-frequency vibration isolator with quasi-zero stiffness (QZS) based on a symmetric link-rod-type structure. The principle of the isolator is analyzed, and the properties of the vibration isolator are investigated experimentally. Varying displacements with a restoring force and stiffness are acquired by a static model; thus, the QZS conditions and system contributing factors are elucidated. Various effects of the excitation amplitude, damping ratio, rod length ratio, and initial spring compression ratio on the displacement transmissibility, which are determined using the harmonic balance method (HBM), are discussed. Through a series of experiments on the isolator prototype, the performance of a QZS vibration-isolation system with a symmetric link-rod-type structure is validated. The results indicate that the presented symmetric link-rod-type QZS vibration isolator has a wider QZS interval, lower frequency of vibration isolation, and better isolation performance, providing a valuable reference for the design of QZS vibration isolators.

Reliability-based design optimization scheme of isolation capacity of nonlinear vibration isolators

Nonlinear vibration isolators (NVIs) are beneficial to isolate or suppress the adverse effects caused by harmful vibration. To a large extent, the isolation capacity of NVIs depends on the selection of design parameters (including structural, geometric, and excitation parameters) of vibration isolators. However, existent uncertainties of these parameters are unavoidable, which influence the reliability of the isolation capacity of NVIs. In this respect, an effective reliability-based design optimization (RBDO) scheme of isolation capacity of NVIs is presented by taking into account the parameter uncertainties of NVIs. In the proposed RBDO scheme, the force transmissibility of nonlinear isolators is regarded as the objective function, and the fundamental frequency, the dynamic displacement response amplitude, and reliability of vibration isolation performance are supplied as the constraints to search the optimal design parameters of NVIs. Considering the influence degree of design parameters uncertainties, the global reliability sensitivity analysis is employed for identifying the critical design parameters in NVIs. A surrogate model of the failure probability function is established by the adaptive learning Kriging approach to decrease the computational cost of the reliability evaluation nested in the RBDO scheme. An advanced meta-heuristic algorithm is executed to search for the design parameters for optimal isolation capacity of NVIs. The proposed scheme provides a potential direction for optimizing the isolation capacity of complicated vibration isolators.

Numerical and experimental investigation of a high-static-low-dynamic stiffness vibration isolator with tunable stiffness and damping

Nonlinear vibration isolators that take advantage of negative stiffness elements can simultaneously meet the requirements of acceptable static deflection and frequency band of isolation and are thus superior to their linear counterparts. Incorporating electromagnetic elements into the vibration isolator is a common approach to provide the required negative stiffness. Electromagnetic mechanisms are low-cost, tuneable, and operate without friction. Also, they can extract or dampen the energy of the host system through electromechanical coupling. Therefore, electromechanical elements are ideal choices for designing multi-purpose vibration control mechanisms. In this study, three coils surrounded by arrays of permanent magnets are considered. When the system vibrates, their magnetic fields interact with that of a moving magnet attached to a rod supporting an isolated mass. The electromagnetic properties of the proposed system are simulated using the finite element method (FEM) and experimental measurements are used to validate the numerical simulations. Different scenarios for a system consisting of three coaxial coils are considered and compared, including powering the coils, open circuit coils, short circuit coils and coils shunted with an external circuit. Features of each case are discussed and general guidelines for designing a multipurpose vibration controller are given.

Research and Application of Vibration Isolation Platform Based on Nonlinear Vibration Isolation System

In order to weaken the ground vibration caused by mechanical equipment, a vibration isolation platform of nonlinear vibration isolation system is proposed. The influence of flexible foundation and nonlinear isolator parameters on the performance of nonlinear vibration isolation platform is studied. By optimizing the nonlinear parameters of the vibration isolation platform, the vibration response of equipment vibration is effectively blocked. The research results show that the structural parameters such as stiffness and damping of the nonlinear vibration isolation system affect the vibration mode of the vibration isolation platform, thus affecting the vibration response of the whole system. Applying the nonlinear vibration isolation system to the project, the impact of the vibration of the refiner on the vibration of the floor is greatly reduced. It shows that this method can be used to reduce the foundation vibration caused by the equipment, improve the operation status of the equipment, and increase the safety factor of the building.

A study of a nonlinear vibration isolator supported on an imperfect boundary plate

The research on the nonlinear vibration isolation of continuum systems always focuses on the perfect boundary conditions. In this work, nonlinear isolation of transverse vibrations of the arbitrary boundary rectangular plate was investigated. A novel analytical approach was proposed. The rigid body dynamics and high-order energy Fourier series expansion method were utilized to establish a mathematical model of the arbitrary boundary nonlinear continuum system. This method involves the simultaneous Fourier series expansion in temporal and spatial domains. The dynamic behaviors of an arbitrary boundary rectangular plate with nonlinear vibration isolators can be described through a harmonic balance analysis together with arc-length continuation. The convergence and stability for the frequency response functions were checked via the Lyapunov stability theory. The numerical results supported the analytical solutions. Both the analytical and numerical results demonstrated that nonlinear broadband vibration isolation is sensitive to the elasticity of the arbitrary boundary flexible foundation. Furthermore, increasing damping can effectively suppress the transmission of low-order vibrations and control the divergence of higher-order vibrations. Finally, an experiment rig was designed to validate the nonlinear isolation of the transverse vibrations of an arbitrary boundary plate.

Parametric study of the axial force and negative stiffness of an electromagnetic mechanism for vibration isolation applications

Nonlinear vibration isolators that take advantage of negative stiffness elements can provide high static stiffness to bear high static loads and quasi-zero dynamic stiffness to widen the isolation frequency band and hence are desirable for vibration isolation. Electromagnetic negative stiffness elements can be used to design and fabricate quasi-zero-stiffness vibration isolators. Different combinations of permanent magnets and electromagnetic coils in attractive or repulsive configurations can lead to negative stiffness. The magnitude of the electromagnetic restoring force and negative stiffness is dependent upon many geometric and electromagnetic parameters and is controllable by adjusting the current in the electromagnetic coils. The present work compares the negative stiffness properties of three different configurations and provides a general guideline for selecting the appropriate configuration. The finite element method is used to simulate the magnetic fields and electromagnetic force acting on the permanent magnet. Numerical results are presented, and findings are validated by analytical solutions.

A nonlinear quasi-zero stiffness vibration isolator with quintic restoring force characteristic: A fundamental analytical insight

The nonlinear mechanical oscillator with X-shaped-spring suspension has attracted relevant attention in the past couple of years due to its ability to tailor the corresponding stiffness characteristic on purpose and fit diverse engineering needs. This paper deeply investigates the conditions for such a configuration to exhibit a quasi-zero stiffness behaviour with both the linear and cubic elastic term of the force-displacement curve equal to zero. The resulting quintic characteristic leads to a vibration isolator with a much larger isolation frequency band respect to the classical isolator with non-zero cubic elastic term only. A systematic comparison between the quintic and cubic characteristics is performed, emphasizing the asymptotic trends, and thus showing the fundamental behaviours. It is found that the critical damping for an unbounded response of the quintic isolator is proportional to the square of the normalized excitation amplitude, while that of the cubic isolator is directly proportional to the normalized displacement amplitude. This makes the critical damping of the quintic isolator much lower, and thus more favourable in practical engineering applications, where the values of the normalized excitation amplitude are less than one.

Nonlinear Vibration Isolation of Spacecraft System by a Bionic Variable-Stiffness Device Enhanced by Electromagnetic Component

Nonlinear Vibration Isolation of Spacecraft System by a Bionic Variable-Stiffness Device Enhanced by Electromagnetic Component

Design and correlation analysis of quasi-zero stiffness passive vibration isolation air spring

Vibration isolation systems are widely used in high-end automobile manufacturing, precision instrument processing, building and bridge seismic resistance, ship machinery noise reduction and other engineering fields, with good development prospects. At present, the existing vibration isolation systems on the market are mainly divided into active and passive vibration isolation systems. Passive vibration isolation does not require external energy input. Its structure is simple and the control scheme is easy to implement. However, passive vibration isolation performs well in high frequency vibration but not in low frequency. As a new nonlinear low-frequency vibration isolation technology, the quasi-zero stiffness vibration isolation system has changed the traditional concept of linear system vibration isolation. In addition, compared with traditional spring, air spring as a new type of elastic vibration isolation mechanism has many excellent performances, such as high fatigue resistance and high stiffness. Therefore, this paper uses air spring to design a passive vibration isolation quasi-zero stiffness air spring structure with good vibration isolation effect, simple structure and low cost in both low-frequency and high-frequency vibration.

Analysis on nonlinear stiffness isolators revealing damping thresholds

Nonlinear vibration isolators with stiffness nonlinearity show promise for a broadband isolation performance without degrading the load capacity. An analytical method is proposed to predict all the possible frequency responses of nonlinear stiffness isolators under different damping. The vibration equation is transformed into an algebraic equation through harmonic balance method. The equation is regarded as a function of the frequency instead of the amplitude, leading to a general analytical method with its complexity independent with the order of the nonlinear stiffness. A damping threshold function is proposed based on the root conditions of the frequency, and the whole damping region is divided into large damping, medium damping and small damping sub-regions accordingly. The root conditions and the frequency responses in each sub-region are analytically analyzed. All the possible responses are classified into five categories based on the damping thresholds and the existence of a jump phenomenon. Nonlinear phenomena of full-band isolation, bounded response and unbounded response are revealed according to multivalued roots of the frequency, and their sufficient and necessary conditions are presented. Simulations are performed on nonlinear isolators with cubic stiffness, high-order stiffness, and non-polynomial stiffness, respectively. The damping thresholds, frequency response categories, and the nonlinear characteristics of each category are demonstrated for the studied cases. A high-order harmonic balance method and the Runge–Kutta method are adopted to verify the effectiveness of the proposed method. This work presents a general analytical method for the prediction of frequency responses, the determination of damping thresholds, and the theoretical illustrations of unique behaviors for nonlinear stiffness isolators.

Competitive advantages of a bistable vibration isolator: Cut-off frequency and operational safety near harmful resonance

This study reveals the competitive advantages of a bistable vibration isolator over conventional linear and monostable ones. Generally, reducing stiffness improves vibration isolation performance with a lower cut-off frequency but for the linear vibration isolators involves a large-amplitude oscillation. Nonlinear monostable and bistable vibration isolators have been developed to resolve the contradictory issue of the linear case, reducing both the cut-off frequency and the range of oscillation. However, it has not yet been determined what advantages make a bistable vibration isolator more promising than a monostable one. In this study, equivalent linear, monostable, and bistable vibration isolators were found, and their numerical and theoretical dynamic responses compared directly. First, the cut-off frequency tended to be lower in the order of the bistable, equivalent linear, and monostable vibration isolators. In other words, the bistable system provides a wider vibration isolation bandwidth than the equivalent linear one, whereas the monostable one makes it narrower. Second, the bistable vibration isolator enhanced operational safety in the amplification region thanks to its small force transmissibility, while the monostable one exacerbated the risk. Bifurcation analyses of the nonlinear steady-state oscillations of the bistable and monostable vibration isolators were also performed to identify and investigate the dangerous and safe amplification regions. The results of the analyses clearly demonstrated the superior operational safety of the bistable vibration isolator, particularly in terms of a larger safety margin in the amplification region.

Shock Isolation of an Orthogonal Six-DOFs Platform With High-Static-Low-Dynamic Stiffness

Abstract A novel approach to enhance the shock vibration environment of multi-directions using a high-static-low-dynamic stiffness supported orthogonal six-degrees-of-freedom (DOFs) nonlinear vibration isolation (OSNVI) system is presented in this paper. By combining spring positive stiffness and magnetic negative stiffness, the proposed system achieves high-static-low-dynamic stiffness. Under the multi-directions half-sine vibration, the dynamic equation of the OSNVI is obtained. Both dynamic and static analysis methods are utilized to explore the effect of various parameters on the shock isolation performance of the OSNVI from both the time and frequency domains. The results indicate that the proposed OSNVI can efficiently suppress multi-direction shocks at the cost of only one second. Although a nonlinear jump is usually not expected, the nonlinear jump of the OSNVI could improve the load capacity by increasing the spring stiffness without changing the shock isolation frequency band. Finally, a shock experiment is employed through a three-axis shaker platform to validate the shock isolation performance of the orthogonal six-DOF nonlinear vibration isolator. The proposed OSNVI provides a promising approach to suppress the multi-directional shock vibrations.

Design and experimental study of a two-stage nonlinear vibration isolators with quasi-zero stiffness

Quasi-zero-stiffness (QZS) vibration isolators are practical solutions for isolation in the low-frequency range. However, single-layer QZS isolators have a low roll-off rate of transmissibility in the frequency band of isolation, especially at high frequencies. The purpose of this study is to design a novel two-stage QZS isolator, called TSQZS isolator. In each stage, the quasi-zero stiffness is achieved by combining magnetic rings and linear springs in parallel. The TSQZS isolator can support a wide range of payloads by adjusting the initial compression of the positive-stiffness element (coil spring). Firstly, an analytical model of magnetic spring is given by employing the theory of equivalent magnetic charge, and the parameters are designed using the finite element simulation. Then, the dynamic behaviors of the TSQZS isolation system are revealed by using the harmonic balance method, and the isolation performance is assessed by displacement transmissibility. Finally, an experimental prototype is fabricated and the experimental testing setup is established to verify the isolation performance of the TSQZS system under base excitation. The results demonstrate that the devised TSQZS isolator not only enables vibration isolation at low frequencies, but also gains a high roll-off rate of transmissibility in the frequency band of vibration isolation.

Design and Development of Structural Parameter Identification Software for Nonlinear Vibration Isolators

This paper developed an object-oriented software to facilitate parameter calibration of the quasi-zero stiffness (QZS) vibration isolator for engineering applications. Considering its advantages of convenient programming and high noise resistance, we employ the harmonic balance method to construct the identification core algorithm. The developed software consists of data pre-processing, parameter identification, and post-processing modules. The data pre-processing module imports and classifies all the required data. Then, the parameter identification module conducts preliminary nonlinearity analysis so that nonlinear structural parameter identification can be successfully carried out. After parameter identification, the data post-processing module displays and stores the identified results. The performance of the software is tested by a numerical example of a two-degree-of-freedom QZS vibration isolator, proving the software can give accurate identification results within a few user-friendly graphical interfaces. Based on this software, we hope that the application and promotion of nonlinear system parameter identification become more convenient.

Analysis of super-harmonic resonance and periodic motion transition of fractional nonlinear vibration isolation system

The precision instruments and equipment are often utilized in low-frequency and micro-amplitude vibration systems, in which many vibration isolators of rubber materials are widely used. Ignoring the low-frequency amplitude will result in errors in the fatigue life design of the vibration isolators and predicting the dynamic response of each frequency band accurately becomes necessary. However, integer-order models cannot describe the frequency dependence of rubber materials, while the fractional-order models can describe it instead. On the other hand, the elastic restoring force is strongly nonlinear under large deformation, and the vibration of the nonlinear system contains multiple harmonic components. In order to solve those issues, the fractional nonlinear Nishimura model is used to characterize the constitutive relation of vibration isolators such as air springs, which are made of carbon black filled natural rubber. The high-order harmonic balance method is used to obtain the steady-state response of the vibration system, while the fourth-order Runge–Kutta method is applied to simulate the dynamic response of the system in the low-frequency region, and the Lyapunov exponent is used to determine the stability of the system. Furthermore, the influence of parameters on the amplitude–frequency characteristics of different frequency bands is also studied, and a method to solve the optimal damping coefficient is proposed based on the primary resonance amplitude–frequency curves. The results show that there is a diversity of periodic motions in the process of adjacent super-harmonic resonance transition. Numerical simulations also demonstrate that multi-periodic motions coexist in the system. The motion transition law between the polymorphic coexistence region and its adjacent regions is summarized.

Performance of a shock isolator inspired by skeletal muscles

Nonlinear vibration isolators with low dynamic stiffness have advantages compared to linear isolators, but they also have limitations in terms of the maximum allowable displacement around a chosen equilibrium position. To overcome this issue, a novel nonlinear isolator is proposed that outperforms the classical quasi-zero stiffness nonlinear isolator when large inputs are applied. In this paper, the response of the isolator when subject to shock excitation is investigated. The isolator suspension is designed to exhibit a quasi-static force-deflection curve with sigmoidal shape, which has been observed in many studies reporting the characteristics of skeletal muscles. The shape of the force-deflection curve is such that the suspension system can store greater elastic potential energy. Simulations show that the proposed four-spring system outperforms the classical nonlinear three-spring configuration, in terms of maximum displacement of a suspended mass, when the shock amplitude is relatively large. This is achieved by exploiting the softening effect for large deformations.