Nonlinear response of a multidirectional negative-stiffness isolation system via semirecursive multibody dynamic approach

This paper investigates an innovative negative-stiffness device(NSD)that modifies the apparent stiffness of the supported structure for seismic isolation.The NSD comprises a lower base on the bottom and a cap on the top,together with a connecting rod,vertical movable wall,and compressed elastic spring,as well as circumferentially arranged,pretensioned external ropes,and inclined shape memory wires.This configuration can deliver negative stiffness and energy dissipation in any direction within the horizontal plane.A numerical model of the device is developed through a two-step semirecursive method to obtain the force–displacement characteristic relationship.Such a model is first validated through comparison with the results obtained via the commercial software ADAMS.Finally,a large parametric study is performed to assess the role and the influence of each design variable on the overall response of the proposed device.Useful guidelines are drawn from this analysis to guide the system design and optimization.

偏载作用下菱形负刚度隔振系统的刚度特性

为探究偏载对菱形负刚度隔振系统刚度的影响,课题组基于力学分析方法,建立了偏载作用下隔振系统的数学模型,得到其无量纲刚度-位移非线性曲线,分析了偏载对其准零刚度特性的影响。利用Simulink进行仿真实验,给偏载作用下的隔振系统振动基座施加激励,得到了不同激励下隔振系统的时变刚度;结合傅里叶变换,探讨了隔振系统刚度的时变特性和幅频特性。结果表明:偏载越大,低刚度区间越窄,准零刚度特性越弱;时变刚度波动范围与峰值随偏载的增加而变大,但时变刚度的波动趋势不受偏载的影响;时变刚度幅值主要集中在低频区间,随频率的增加而减小,最终趋近于0。研究表明偏载对隔振系统的刚度会产生一定的影响。

A quasi-zero stiffness energy harvesting isolator with triple negative stiffness

Vibration isolation for low frequency excitation and the power supply for low power monitoring sensors are important issues in bridge engineering.The main problem is how to effectively combine the vibration isolator with the energy harvester to form a multi-functional structure.In this paper,a system called quasi-zero stiffness energy harvesting isolator(QZS-EHI)with triple negative stiffness(TNS)is proposed.The TNS structure consists of linear springs,rigid links,sliders,and ring permanent magnets.Newton’s second law and Kirchhoff’s law construct dynamic equations of the QZS-EHI,and a comparison is made to contrast it with other QZS and linear isolators.The comparison field includes the QZS range,amplitude-frequency relationship,force transmissibility,and energy harvested power.The isolator can be applied to many engineering fields such as bridges,automobiles,and railway transportation.This paper selects bridge engineering as the main field for the dynamic analysis of this system.Considering the multi-span beam bridge,this paper compares different situations including the bridge with QZS-EHI support,with linear stiffness isolator support,and with single beam support.All results show that the QZS-EHI is not only better than the traditional isolator with linear stiffness under both harmonic and stochastic excitation,but also better than some QZS isolators with double or single negative stiffness in bridge vibration isolation and energy harvesting.Theoretical analysis is verified to correspond to the simulation analysis,which means the proposed QZS-EHI has practical application value.

High-static-low-dynamic stiffness isolator based on an electromagnetic negative stiffness spring with long linear stroke

Negative stiffness mechanisms can improve low-frequency vibration isolation performance and have been widely used in the vibration isolation of precision equipment. However, the negative stiffness mechanism usually introduces a nonlinear stiffness,resulting in a nonlinear response and worsening the vibration isolation performance, especially under large amplitude vibration.In this paper, an electromagnetic spring with linear negative stiffness(ESLNS) is proposed, in which the antagonistic ampere forces of the energized coils are used to generate negative stiffness within a long linear stroke. The magnetic field distribution is improved through the design of the magnetic circuit, thereby increasing the stiffness generation efficiency. The stiffness can be adjusted bidirectionally by current within the range of positive and negative stiffness. An electromagnetic stiffness model was established based on the equivalent magnetic circuit method. Experimental measurements verified the accuracy of the model and proved the linearity of the electromagnetic spring. A vibration isolator with high static and low dynamic stiffness(HSLDS) based on the ESLNS is designed and tested. The experimental results prove that the introduction of the ESLNS can effectively expand the isolation frequency band without changing the equilibrium position. Moreover, the vibration isolator with ESLNS does not produce nonlinear response. The proposed electromagnetic spring with linear negative stiffness extends the application range of HSLDS isolators to a large amplitude vibration environment.

一种准零刚度系统隔振性能的几何参数优化分析

提出了一种采用菱形连杆组件作为负刚度机构的准零刚度隔振器(下文简称菱形准零刚度隔振器)。通过静力学分析方法,建立了菱形准零刚度隔振器数学模型,并与其他调节变量较少的隔振器模型进行了对比;以被测量曲线在隔振器平衡位置处的曲率作为评价参数,研究了负刚度机构几何参数对系统刚度、阻尼非线性的影响,推导了利用几何参数进行隔振优化的条件;采用谐波平衡法求解系统动力学方程,对隔振器在不同几何参数下的隔振性能进行了分析。结果表明:菱形准零刚度隔振器具有体积相对较小且非线性调节能力较好的特点,可通过调节杆长,或满足相关临界值条件时调节杆长偏差量(下文简称杆长差)对刚度及阻尼非线性特征进行优化;刚度与阻尼的非线性优化方向不同,但通常情况下,刚度非线性因素对隔振优化起主导作用;归一化振动相对位移小于0.1时,由刚度曲线曲率得到的临界值可以较好地作为杆长差参数的隔振优化调节依据。本文提出的非线性评价方法与几何非线性优化临界值计算方法,对于类似隔振器研究和设计具有一定的指导意义。

菱形HSLDS隔振器负刚度机构质量及摩擦力影响分析

以菱形负刚度机构HSLDS(high static low dynamic stiffness)隔振器(简称菱形HSLDS隔振器)为研究目标,采用虚功法建立负刚度机构等效摩擦力模型,并以拉格朗日方法建立包含负刚度机构质量及摩擦力因素的动力学方程;利用谐波平衡法(HBM)求解动力学方程,分析了负刚度机构质量及摩擦力对隔振的影响及其优化措施,并通过实物样机验证了理论模型的合理性。实验结果表明:负刚度机构质量及摩擦力对隔振均产生不利影响,应尽量减小;将负刚度机构连杆较短侧连接于载荷平台端,可以减小负刚度机构质量对较高频段隔振性能的影响;在限定隔振器刚度参数以及铰接副接触参数且同时满足刚度与摩擦力优化条件下,通过增大连杆机构杆长差的方式可以优化低频段隔振性能,并降低负刚度机构摩擦力对高频段隔振的影响。

Design of a combined magnetic negative stiffness mechanism with high linearity in a wide working region

Combining magnetic negative stiffness mechanism(NSM) in parallel with positive stiffness has been considered to be an effective approach to realize the quasi-zero stiffness(QZS) characteristic,thus resolving the contradiction between high load capacity and(ultra-) low-frequency vibration isolation capability.However,the remarkable stiffness nonlinearity of common magnetic NSMs restricts the displacement region with reliable negative stiffness,resulting in considerable nonlinear behavior,poor vibration attenuation performance,and probable instability under large amplitude vibrations.A novel combined negative stiffness mechanism(CNSM) with attractive magnetic NSM(ANSM) and repulsive magnetic NSM(RNSM) in parallel is proposed in this paper.The stiffness nonlinearities of the ANSM and RNSM in the CNSM are counteracted through the parallel configuration such that the displacement region with reliable linear stiffness of the CNSM is widened by several times.An analytical model of the CNSM is established by the magnetic charge model and verified by simulation on ANSYS Maxwell.Parametric studies are then conducted to investigate the effects of design parameters on the stiffness characteristic,providing guidelines for the optimal design of the CNSM.Meanwhile,the stiffness and nonlinearity of the CNSM are compared with that of a single ANSM and RNSM.Static and dynamic experiments are finally conducted on the proposed test prototypes.Experimental results demonstrated the validity of the established model and the effectiveness of the CNSM in generating high linear stiffness within a wide displacement region and lowering the resonance frequency.Thus,the proposed CNSM can be applied in(ultra-) low-frequency vibration isolation under large amplitude excitations.