Nonlinear Vibration Isolation System Research Articles

Approximate Response of a Non-linear Vibration Isolation System Using the Harmonic Balance Method

Approximate Response of a Non-linear Vibration Isolation System Using the Harmonic Balance Method

Improvement of vibration isolation performance of QZS platform in chaotic interval based on damping increase control method

In order to further extend the effective isolation range of the quasi-zero stiffness (QZS) platform, the vibration isolation performance of the chaotic interval is improved. For a class of self-design quasi-zero-stiffness (QZS) vibration isolation platform, starting with chaotic motion of the non-linear vibration isolation system, the jumping interval is eliminated by means of transient chaos phenomena. The control method of damping increase is proposed in combination with the application of the Von der Pol Plane, which can make the jumping-down frequency to be decreased below the external excitation frequency, thus the effective isolation range of vibration isolation platform can be extended, and a lower isolation frequency can be obtained. Research shows that, when the solution of the motion equation of the platform system falls to resonant branch led by certain initial conditions, the resonant amplitude response will jump to the non-resonant branch by transient damping increase control method, which the removal time is determined by the Von der Pol Plane, hence making the platform system obtain the ideal vibration isolation performance. The research results have a significant importance for improving the low frequency and ultra-low frequency vibration isolation effect of such platforms, which lays a foundation for the popularization and engineering application, and can also provide a reference for control of other nonlinear vibration system.

Vehicle Vibration Safety Evaluation in the Time Domain

The article is a sequel to studies of the nonlinear vibration isolation systems of a vehicle. The first published papers considered an application of the known methods of statistical linearization when determining the vibration safety performance in the frequency domain. The frequency domain is the most adaptive in the context of analysis of the obtained calculation results and evaluation of the initial dynamic system features. Therefore, a problem to determine the adequacy range of such calculations in the frequency and time domain is relevant.The paper deals with the problem of creating a technique to determine and analyze the spectral characteristics of the vehicle vibration isolation system when modeling in the time domain. Considers as an object, a nonlinear dynamic system equivalent to the nonlinear vibration isolation system of a vehicle under its spatial vibrations. In formulating a system of equations-of-motion of the adopted system a module-based method was used. As an example, the power unit is given. Modeling of input random perturbations, provided that the solutions obtained are adequate, is based on the recurrent difference equations. The subsequent transformation of the calculation results into the frequency domain is based on the finite Fourier transforms.To determine the final parameters which characterise the effectiveness of the vibration isolation system, at the first stage of calculations the dynamic system was tested in a linear setting.The vector of natural frequencies of a conservative system defined in the frequency domain was compared with the spectrum of natural frequencies (the frequency response) calculated in the time domain. Besides, the article has carried out a conformity evaluation of the amplitude-frequency characteristics obtained in the frequency and time domain and their determining accuracy. The obtained positive results made it possible to compare and analyze the spectral characteristics of vibration signals and dynamic system in its nonlinear and linearized formulation. The coherence function, the amplitude-frequency characteristic, the spectral density of perturbation and output vibration signal, the vehicle suspension and tyre load characteristics are considered as the analyzed ones. The article compares the output characteristics of the dynamic system under consideration for the case in linear, linearized, and nonlinear formulation of the problem.

Analysis of systems with nonlinear auxiliary mass dampers by means of a special selection of linear generating functions

Nonlinear vibration isolation systems have a wider range of effective damping than linear ones. However, their analysis with an arbitrary load is quite laborious. In the article the method of special selection of linear generating systems for analyzing nonlinear systems proposed by professor Chernov Yu T is used. The linear generating system is chosen in such a way that the difference between the solutions of the linear and nonlinear systems in the first approximation for the first harmonic is minimal. Such an approach makes it possible to reduce the complexity of constructing the amplitude-frequency characteristics of nonlinear systems. In this paper, the amplitude-frequency characteristics were constructed to evaluate the efficiency of nonlinear auxiliary mass dampers at different frequencies of the external load. Tuned mass damper (TMD) was chosen as the type of auxiliary mass damper. The article looks at numerical examples of two systems with nonlinear TMD as a three degrees of freedom system. In the first numerical example, a stand with an equipment installed on it was analyzed. The TMD is installed on the stand. In the second numerical example the equipment is installed on a pedestal. The equipment is equipped with a nonlinear TMD. In both examples, there is cubic reaction-displacement relationship in the link that attaches the TMD. The amplitude-frequency characteristics for both systems are constructed for different variants: with a nonlinear, linear TMD and without a damper. The linear TMD was tuned to the first natural frequency of oscillations of the system without a damper. A comparative analysis of the options is given. The efficiency of using nonlinear TMD is determined from the numerical examples. There is a three times reduction in displacements in the nonlinear system as compared to the linear system.

Analysis of the non-resonance of nonlinear vibration isolation system with dry friction

We studied the properties of cubic nonlinear systems with dry friction damping on the prospect of ‘non-resonance’. An approximate method was used to get the frequency-response function. And the critical dry friction which ensures no displacement transmissibility amplified in whole frequency range was determined through the frequency-response function. We also researched those characters which may influence the effect of the non-resonance in this system, and proved those results by empirical experiments. The above conclusions have a theoretical significance for the design of nonlinear vibration isolators.

Study on the dynamics of two-degree-of-freedom system with variable stiffness magnetic isolator

This paper presents a novel variable stiffness isolator designed by magnetic springs in parallel with linear positive stiffness spring. Firstly, the two-degree-of-freedom vibration system model with variable stiffness magnetic isolator is established. The amplitude frequency characteristic equation of the system is derived based on the multi-harmonic method, and the corresponding curve of the relationship between the amplitude and frequency is given. The influence of the current on the curve is researched. Results showed that there are two pseudo-resonant peaks in the amplitude–frequency curve, and one is in the low frequency band, the other exists in higher frequency band. The first peak does not exhibit the frequency shift, but the second one bends to the natural frequency obviously. With the increasing of the current, the peaks decrease and the backbone curve changes greatly for the second resonant crest. The Lyapunov exponent curve around the resonant frequency is calculated. It is shown that there is chaotic parameter region for the system, and chaos can be controlled with the variable stiffness magnetic vibration isolator according to this research, which is beneficial to the design of nonlinear vibration isolation system.

Parameter design of a multi-delayed isolator with asymmetrical nonlinearity

In this study, based on the analysis of multiple nonlinear vibration properties, the criterions of parameter design for different types of excitations and structural nonlinearities are proposed for vibration isolation. For a nonlinear vibration isolation system with Quasi-Zero-Stiffness property, the assembly process and stiffness property with different masses of isolation object are taken into account. In order to improve the isolation effectiveness in a wide frequency band, the relation between vibration performances and parameters is established. The effect of adjustable parameters on the vibration features and the effect mechanisms of multiple time delays are discussed in details based on the method of multiple scales. Because the study takes full consideration of the effect of structural nonlinearity and transition mechanism of vibration performances, the proposed criterions for parameter design could solve the conflict between the improvement of isolation effectiveness and complexity or bifurcation brought by nonlinearity. The results in this paper show that without changing the High-Static-Low-Frequency advantage brought by the nonlinear isolation structure, the isolation effectiveness could be improved in a wide frequency band.

Power Flow in a Two‐Stage Nonlinear Vibration Isolation System with High‐Static‐Low‐Dynamic Stiffness

The manuscript concerns the power flow characterization in a two‐stage nonlinear vibration isolator comprising three springs, which are configured so that each stage of the system has a high‐static‐low‐dynamic stiffness. To demonstrate the distinction of evaluation for vibration isolation using power flow, force transmissibility is used for comparison. The dynamic behavior of the isolator subject to harmonic excitation, however, is of interest here. The harmonic balance method (HBM) could be used to analyze the frequency response curve (FRC) of the strong nonlinear vibration system. A suggested stability analysis to distinguish the stable and the unstable HBM solutions is described. Increasing both upper and lower nonlinear stiffness could bend the first resonant peak to the left. The isolation range in the power and the force transmissibility plot could be extended to the lower frequencies when the nonlinear stiffness is increased, but the rate of roll‐off for the power transmissibility is twice the rate for the force transmissibility at each horizontal stiffness setting. An explanation for this phenomenon is given in the paper.

Experimental Investigation of a Two-Stage Nonlinear Vibration Isolation System With High-Static-Low-Dynamic Stiffness

A novel design of a two-stage nonlinear vibration isolation system, with each stage having a high-static-low-dynamic stiffness (HSLDS), is studied experimentally in this paper. The positive stiffness in each stage is realized by a metallic plate, and the corresponding negative stiffness is realized by a bistable carbon fiber–metal (CF) composite plate. An analytical model is developed as an aid to design a bistable composite plate with the required negative stiffness, and a static test of the plate is conducted to measure the actual stiffness of the plate. Dynamic tests of the two-stage isolator are carried out to determine the effectiveness of the isolator. Two tests are conducted, one with the bistable composite plates removed so that the isolator behaves as a linear device and one with the bistable composite plates fitted. An improvement in the isolator transmissibility of about 13 dB at frequencies greater than about 100 Hz is achieved when the bistable composite plates are added.

On the transmissibilities of nonlinear vibration isolation system

Transmissibility is a key parameter to quantify the effectiveness of a vibration isolation system. Under harmonic excitation, the force transmissibility of a linear vibration isolation system is defined as the ratio between the amplitude of the force transmitted to the host structure and the excitation force amplitude, and the displacement transmissibility is the ratio between the displacement amplitude of the payload and that of the base. For a nonlinear vibration isolation system, the force or the displacement responses usually have more frequency components than the excitation. For a harmonic excitation, the response may be periodic, quasi-periodic or chaotic. Therefore, the amplitude ratio cannot well define the transmissibility. The root-mean-square ratio of the response to the excitation is suggested to define the transmissibility. The significance of the modified transmissibility is highlighted in a nonlinear two-stage vibration isolation system consisting of two linear spring connected linear vibration isolators with two additional horizontal linear springs. Harmonic balance method (HBM) is applied to determine the responses with the fundamental and third harmonic. Numerical simulations reveal that chaos may occur in the responses. In both cases, the modified transmissibility works while the original definition cannot be applied to chaotic response.

Stochastic resonance in a nonlinear mechanical vibration isolation system

This paper concerns the effect that a stochastic resonance can have on a vibration isolation system. Rather than reducing the transmitted force, it is shown that it is possible to significantly mask the component of the force transmitted though the isolator, when the system is excited harmonically. This can be achieved by adding a very low intensity of random noise to the harmonic excitation force. The nonlinear mechanical vibration isolation system used in the study consists of a vertical linear spring in parallel with two horizontal springs, which are configured so that the potential energy of the system has a double-well. Prior to the analytical and numerical study, an experiment to demonstrate stochastic resonance in a mechanical system is described.

Comparison of Linear and Nonlinear Vibration Isolation System under Random Excitation

This article studies and compares the efficiency of linear and nonlinear vibration isolation systems. The estimation relies on the value of isolated mass standard deviation due to external oscillation with different spectral densities. The solution of nonlinear differential equation of isolated by nonlinear vibration isolator mass is based on harmonic linearization method. External excitation process is treated as white noise wideband process with different spectral densities. The main interest is attached to the definition of vibration criteria exceedance number for the isolated mass suspended on both types of vibration isolators. The article suggests the application of several practical formulas of exceedance number calculation.

Determining the Amplitude–Frequency Response and Settings of a Nonlinear Vibration Isolation System with a Quasi-Isochronous Damper

Algebraic equations of the first order describing the amplitude–frequency response of a nonlinear vibration isolation system with a quasi-isochronous roller damper are derived. A numerical experiment is conducted using these equations. A combined graphical/numerical method to find the optimal settings for this damper is proposed. It is established that the natural frequencies of the optimally tuned damper do not coincide in the nonlinear and linear cases. It is shown that the new quasi-isochronous roller damper can substantially decrease the amplitude of forced vibrations

Research on modeling of nonlinear vibration isolation system based on Bouc–Wen model

Abstract A feedforword neural network of multi-layer topologies for systems with hysteretic nonlinearity is constructed based on Bouc–Wen differential model. It not only reflects the hysteresis force characteristics of the Bouc–Wen model, but also determines its corresponding parameters. The simulation results show that restoring force–displacement curve hysteresis loop is very close to the real curve. The model trained can accurately predict the time response of system. The model is checked under the noise level. The result shows that the model has higher modeling precision, good generalization capability and a certain anti-interference ability.

Numerical Modelling of Nonlinear Vibration Isolation System Free Oscillations

The article deals with numerical analysis of nonlinear vibration isolation system free oscillations. According to the latest recommendations [1], vibration isolation of precision equipment should be effective over the 1 – 100 Hz range [2]. This fact sets a challenge to develop a sub-herz vibration isolator. Such vibration isolators with 0.5 Hz natural frequency have been developed in latest works [3,4]. For mathematical representation of such a dynamical system, elastic characteristic should be approximated with a polynomial. In this paper, we consider the approximation of elastic characteristic by means of 5th and 7th order polynomials. This leads to numerical solution of nonlinear dynamic equations. We construct the solution of such equation on the phase plane and determine equilibrium points. The stability of the equilibrium points is investigated using linearization technique. The law of the isolated mass oscillations is derived from numerical solution of the dynamic equation by means of Dorman – Prince 4(5) and 8(7) solver and the system’s natural frequencies are calculated using the FFT technique.

Dynamic Analysis of Nonlinear Vibration Isolation System Based on Flexible Foundation

In this paper,a general dynamic model of the isolation coupled system which is composed of isolation object,nonlinear vibration isolation support,and flexible foundation is established,calculated method of applying vibration power flow to analyze isolation effectiveness is studied.Further more,as an calculation example,a air spring vibration isolation system of HS-700 engines is numerically simulated.Designs several low-frequency nonlinear vibration isolators and analyzes its vibration isolation effect.It discusses the effect of the vibration isolator parameters on the transmitted power flow of the system.The results provide a theoretical basis for the optimized design of nonlinear vibration isolation system.

Analysis of Chaotic Characteristics of the Strong Nonlinear Vibration Isolation System Based on Harmonic Balance Method

The key of studying the nonlinear system of the stationary period solutions by the HBM is solving a group of higher order multi-degree-of-freedom nonlinear equations. Aiming at this difficulty, this paper can easily get a higher harmonic balance truncation order expression of solution using a powerful symbolic computation software, and avoid the tedious derivation process. And the main subharmonic response range was accurately obtained by the EACM for solving the nonlinear equations. Meanwhile, the chaotic region was estimated through subharmonic cascade regions combined with the bifurcation of the Feigenbaum rule by solving the system. And, numerical results calculated by the Runge-Kutta method were given to verify the results of the period doubling bifurcations and chaotic region obtained by this method. It has been shown that they are in good agreement.

Numerical investigation on multi-degree-freedom nonlinear chaotic vibration isolation

A chaotic vibration isolation system is designed according to the chaotic vibration theory in this paper. The strong nonlinearity is generated by the system. Line spectra in the radiated noise maybe easily detected caused by marine vessels. It is Important to reduce the line spectra by improving the acoustic stealth of marine vessels. A multi-degree-freedom (MDF) nonlinear vibration isolation system (NVIS) system is setup by the experiment and finite element method. The model is established with finite element method. The results show that the behavior of the device gradually varies from period bifurcation into chaotic state and the line spectrum is changed from single spectral structure into broadband spectral structure. It is concluded that chaotic vibration isolation is preferable contrasted on line spectra isolation.

Examination of super-harmonics in a multi-degree of freedom nonlinear vibration isolation system: Refined models and comparison with measurements

A multi-degree of freedom vibration isolation experiment consisting of a powertrain, three powertrain mounts including a dynamic load sensing hydraulic mount, a sub-frame, and 4 bushings is examined in both time and frequency domains. Since the hydraulic mount exhibits nonlinear phenomena, super-harmonics are observed in motion, pressure and interfacial force measurements when the system is sinusoidally excited. Refined indirect force estimation methods are proposed with a focus on the super-harmonics. This includes the development of a quasi-linear fluid system model with embedded spectrally varying and amplitude-sensitive parameters. The reverse path spectral method is employed using the measured relative motion and upper chamber pressure in the nonlinear hydraulic mount. The relevant transfer functions (with effective parameters for both rubber and hydraulic paths) are used to estimate the interfacial forces. Up to six harmonics of the fundamental excitation frequency are examined, and the contribution of each path is clarified. The proposed quasi-linear fluid system model including super-harmonics extends prior work on indirect force estimation methods and successfully predicts the interfacial forces in the multi-degree of freedom vibration isolation system. The quasi-linear fluid system model, however, seems to be inadequate in estimating the sub-harmonic responses.

Design of vibration isolators by exploiting the beneficial effects of stiffness and damping nonlinearities

Abstract The present study is concerned with the design of a new type of single degree of freedom (sdof) nonlinear vibration isolation system that can deal with harmonic excitations and take advantage of both spring and damping nonlinearities. For typical design requirements expressed in terms of a transmissibility envelope, the proposed design makes use of a recently developed method called the output frequency response function (OFRF) approach, which provides a direct relationship between the system output frequency response and parameters that define the system nonlinearity. Taking all output harmonics into account, a detailed step-by-step procedure is developed to systematically determine the nonlinear parameters from a small set of simulation or experimental data. Simulation studies are conducted to verify the results and demonstrate that the design can effectively achieve all the three requirements for a vibration isolation system of a low resonant peak, low high frequency transmissibility, and a large isolation range.