Force and displacement transmissibility of a quasi-zero stiffness vibration isolator with geometric nonlinear damping

A geometric nonlinear damping is proposed and applied to a quasi-zero stiffness (QZS) vibration isolator with the purpose of improving the performance of low-frequency vibration isolation. The force, stiffness and damping characteristics of the system are presented first. The steady-state solutions of the QZS system are obtained based on the averaging method for both force and base excitations and further verified by numerical simulation. The force and displacement transmissibility of the QZS vibration isolator are then analysed. The results indicate that increasing the nonlinear damping can effectively suppress the force transmissibility in resonant region with the isolation performance in higher frequencies unaffected. In addition, the application of the nonlinear damping in the QZS vibration isolator can essentially eliminate the unbounded response for the base excitation. Finally, the equivalent damping ratio is defined and discussed from the viewpoint of vibration control.     

Effects of anti-symmetric nonlinear viscous damping on the force transmissibility of multi-degree of freedom structures

In the present study, the concept of the output frequency response function is applied to theoretically investigate the force transmissibility of multi-degree of freedom (MDOF) structures with a nonlinear anti-symmetric viscous damping. The results reveal that an anti-symmetric nonlinear viscous damping can significantly reduce the transmissibility over all resonance regions for MDOF structures while it has almost no effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to overcome the dilemma in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant region but increases the transmissibility over non-resonant regions.     

Reducing force transmissibility in multiple degrees of freedom structures through anti-symmetric nonlinear viscous damping

In the present study, the Volterra series theory is adopted to theoretically investigate the force transmissibility of multiple degrees of freedom (MDOF) structures, in which an isolator with nonlinear anti-symmetric viscous damping is assembled. The results reveal that the anti-symmetric nonlinear viscous damping can significantly reduce the force transmissibility over all resonance regions for MDOF structures with little effect on the transmissibility over non-resonant and isolation regions. The results indicate that the vibration isolators with an anti-symmetric damping characteristic have great potential to solve the dilemma occurring in the design of linear viscously damped vibration isolators where an increase of the damping level reduces the force transmissibility over resonant frequencies but increases the transmissibility over non-resonant frequency regions. This work is an extension of a previous study in which MDOF structures installed on the mount through an isolator with cubic nonlinear damping are considered. The theoretical analysis results are also verified by simulation studies.     

The force transmissibility of MDOF structures with a non-linear viscous damping device

In the present study, the concept of the Output Frequency Response Function (OFRF), recently proposed by the authors, is applied to theoretically investigate the force transmissibility of MDOF structures with a cubic non-linear viscous damping device. The results analytically show that the introduction of cubic non-linear damping can significantly reduce the transmissibility over all resonance regions for a Multiple Degree of Freedom (MDOF) structure and at the same time leave the transmissibility over the isolation region virtually unaffected. The analysis also indicates that a strong linear damping may shift the system resonances and compromise the beneficial effects of cubic non-linear viscous damping on the force transmissibility of MDOF structures. This suggests that a less significant linear damping together with a strong cubic non-linear damping can be used in MDOF structures to achieve a desired vibration isolation performance. This research work has a significant implication for the design of viscously damped MDOF structures for a wide range of practical applications.     

Analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems

This study is concerned with the analysis and design of the force and displacement transmissibility of nonlinear viscous damper based vibration isolation systems. Analytical algorithms are derived using the Ritz–Galerkin method to evaluate the transmissibility of SDOF displacement vibration isolation and force vibration isolation systems where a nonlinear viscous damper is used as an energy dissipating device. The results reveal that compared to linear dampers, nonlinear viscous dampers can more significantly improve the system vibration isolation performance in a wider frequency range. A procedure is then proposed based on the analysis results to facilitate the design of nonlinear viscous dampers for system vibration isolation purposes. These results have significant implications for the design of vibration isolation systems in many engineering applications.     

Dynamic analysis and performance evaluation of nonlinear inerter-based vibration isolators

This paper investigates a nonlinear inertance mechanism (NIM) for vibration mitigation and evaluates the performance of nonlinear vibration isolators employing such mechanism. The NIM comprises a pair of oblique inerters with one common hinged terminal and the other terminals fixed. The addition of the NIM to a linear spring-damper isolator and to nonlinear quasi-zero-stiffness (QZS) isolators is considered. The harmonic balance method is used to derive the steady-state frequency response relationship and force transmissibility of the isolators subjected to harmonic force excitations. Different performance indices associated with the dynamic displacement response and force transmissibility are employed to evaluate the performance of the resulting isolators. It is found that the frequency response curve of the inerter-based nonlinear isolation system with the NIM and a linear stiffness bends towards the low-frequency range, similar to the characteristics of the Duffing oscillator with softening stiffness. It is shown that the addition of NIM to a QZS isolator enhances vibration isolation performance by providing a wider frequency band of low amplitude response and force transmissibility. These findings provide a better understanding of the functionality of the NIM and assist in better designs of nonlinear passive vibration mitigation systems with inerters.     

Research on linear/nonlinear viscous damping and hysteretic damping in nonlinear vibration isolation systems

A nonlinear vibration isolation system is promising to provide a high-efficient broadband isolation performance. In this paper, a generalized vibration isolation system is established with nonlinear stiffness, nonlinear viscous damping, and Bouc-Wen(BW)hysteretic damping. An approximate analytical analysis is performed based on a harmonic balance method(HBM) and an alternating frequency/time(AFT) domain technique.To evaluate the damping effect, a generalized equivalent damping ratio is defined w...     

Study of the effects of cubic nonlinear damping on vibration isolations using Harmonic Balance Method

In the present study, Harmonic Balance Method (HBM) is applied to investigate the performance of passive vibration isolators with cubic nonlinear damping. The results reveal that introducing either cubic nonlinear damping or linear damping could significantly reduce both the displacement transmissibility and the force transmissibility of the isolators over the resonance region. However, at the non-resonance region where frequency is lower than the resonant frequency, both the linear damping and the cubic nonlinear damping have almost no effect on the isolators. At the non-resonance region with higher frequency, increasing the linear damping has almost no effects on the displacement transmissibility but could raise the force transmissibility. In addition, the influence of the cubic nonlinear damping on the isolators is dependent on the type of the disturbing force. If the strength of the disturbing force is constant and independent of the excitation frequency, then the effect of cubic nonlinear damping on both the force and displacement transmissibility would be negligible. But, when the strength of the disturbing force is dependent of the excitation frequency, increasing the cubic nonlinear damping could slightly reduce the relative displacement transmissibility and increase the absolute displacement transmissibility but could significantly increase the force transmissibility. These conclusions are of significant importance in the analysis and design of nonlinear passive vibration isolators.     

Bifurcation of rupture path by nonlinear damping force

The linear damping mechanism of the Rayleigh waves is extended to the nonlinear one. Conferring to the model, the analytical method is chosen for the solutions. These solutions depict the unusual bifurcation of the rupture path related to the intersection point of antisoliton and soliton.     

Nonlinear vibration of a slightly curved beam with quasi-zero-stiffness isolators

Nonlinear Dynamics - Bending vibration of isolated structures has always been neglected when the vibration isolation was studied. Isolated structures have usually been treated as discrete systems....     

减振阻尼材料设计方法研究

减振阻尼材料可以改变结构的阻尼特性从而降低振动响应和声辐射水平,因而被广泛应用于飞机结构的减振降噪。本文针对减振阻尼材料的设计和应用开展了一系列试验研究,首先通过材料改性得到了不同主基料下材料的配方对阻尼性能的影响;其次配制了三种不同的约束阻尼结构,通过DMA测试对比了三种约束阻尼结构的最佳使用温度和频率范围;最后对约束阻尼结构的减振效果和粘贴布局应用进行了试验,试验结果表明,约束阻尼结构具有良好的减振效果。通过研究掌握了减振阻尼材料在材料改性、约束阻尼结构设计、粘贴布局应用等方面的一些设计方法,可为后续的进一步研究提供技术支持和参考。     

Controlling the vertical shift of an isolated body based on the vibration of nonlinear systems with asymmetric damping forces

Asymmetric damping forces induce the equilibrium position of the isolated body to shift downward. Inspired by this phenomenon, this paper proposes the novel concept of shifting an isolated body based on the vibration of nonlinear systems with asymmetric damping forces. To verify the feasibility of this concept, a piecewise smooth isolation system is established. The incremental harmonic balance method is used to analyze the nonlinear vibration system and to obtain a steady-state analytical solution. The accuracy of the solution is verified by the Runge–Kutta method. Based on the analytical solution, the influences of some key parameters on the system vibration response are analyzed, revealing that the shift in the isolated body height increases with increasing excitation amplitude and damping asymmetry ratio. Additionally, this shift first increases and then decreases with increasing excitation frequency, reaching a peak near the natural frequency of the intermediate body. Finally, considering the complex structure, high energy consumption, and slow response of active suspension actuators, the proposed concept is applied to the tilt control of a vehicle. The simulation results show that the proposed methodology based on this concept can tilt a vehicle body to a certain angle in the turning direction, enabling the use of a semi-active actuator for vehicle tilt control to realize the control effect achieved by an active actuator.

     

Force transmissibility of a two-stage vibration isolation system with quasi-zero stiffness

Nonlinear Dynamics - A quasi-zero stiffness (QZS) vibration isolator outperforms other passive control strategies in vibration attenuation especially in a low-frequency band, but it also has an...     

Dynamics and isolation properties for a pneumatic near-zero frequency vibration isolator with nonlinear stiffness and damping

Nonlinear Dynamics - Aiming to isolate disturbance vibration for heavy machines with low frequency, a novel hydro-pneumatic vibration isolator with high-static and low-dynamic (HSLD) stiffness is...     

Influence of excitation amplitude on the characteristics of nonlinear butyl rubber isolators

The purpose of this study is to explore the advantages and characteristics of nonlinear butyl rubber (type IIR) isolators in vibratory shear by comparison with linear isolators. It is known that the mechanical properties of viscoelastic materials exhibit significant frequency and temperature dependence, and in some cases, nonlinear dynamic behavior as well. Nonlinear characteristics in shear deformation are reflected in mechanical properties such as stiffness and damping. Furthermore, even when the excitation amplitude is small the response amplitude may often be large enough that nonlinearities cannot be ignored. The treatment involves developing phenomenological models of the effective storage modulus and effective loss factor of a rubber isolator material as a function of excitation amplitude. The transmissibility of a nonlinear viscoelastic isolator is compared with that of a linear isolator using an equivalent linear damping coefficient. Forced resonance vibration and impedance tests are used to characterize nonlinear parameters and to measure the normalized transmissibility. It is found that as the excitation amplitude of the nonlinear viscoelastic isolator increases, the response amplitude decreases and the transmissibility is improved over that of the linear isolator for excitation frequency that exceeds a particular value governed by the temperature and excitation amplitude. The method of multiple scales and numerical simulations are used to predict the response characteristics of the isolator based on the phenomenological modeling under different values of system parameters.     

Cross-section deformation,geometric stiffening,and locking in the nonlinear vibration analysis of beams

Nonlinear Dynamics - Stiff behavior of more general finite element (FE) beam formulations in some problems can be misinterpreted as locking based on comparison with simplified analytical and/or...     

Study of oscillators with a non-negative real-power restoring force and quadratic damping

Oscillators with a non-negative real-power restoring force and quadratic damping are considered in this paper. The equation of motion is transformed into a linear first-order differential equation for the kinetic energy. The expressions for the energy-displacement function are derived as well as the closed form exact solutions for the relationship between subsequent amplitudes. They are expressed in terms of incomplete Gamma functions. On the basis of these results, expressions for the phase trajectories and the loci of maximal velocities are obtained. It is also demonstrated that the time difference between two consecutive relative maxima and minima of the displacement can both increase and decrease with time.     

粘性阻尼土中变截面桩的纵向振动特性与应用研究

考虑土体轴对称波动效应,对变截面桩在任意激振力作用下的纵向振动特性进行了研究。假定桩为竖直、弹性、变截面体,土为线性粘弹性体,其材料阻尼为粘性阻尼。利用拉普拉斯变换,将定解问题转化到拉普拉斯域内求解,通过引入势函数并结合阻抗函数的传递性,得到了拉普拉斯域内的桩顶阻抗函数解析解,进而可得到频域内的桩顶阻抗函数和速度导纳的解析解,利用卷积定理和傅里叶逆变换,求得了半正弦脉冲激振力作用下桩顶速度时域响应半解析解。基于所得解对桩的纵向振动特性进行了分析,重点讨论了桩身截面变化情况对速度导纳曲线和反射波曲线的影响,得到了许多重要结论。