含绞制梁结构的非线性隔振系统建模与仿真

Modelling and simulation of a wire rope based nonlinear vibration isolation system

含绞制梁结构的隔振系统是一种典型的非线性被动隔振系统,依靠绞制梁弹性变形和内部摩擦进行能量转移与耗散。基于两端约束绞制梁结构,构造具有高阶刚度和滞回阻尼的非线性隔振系统,采用Bouc-Wen模型描述滞回恢复力,建立系统在简谐位移激励下的动力学模型。推导隔振系统的等效刚度和等效阻尼比计算公式,等效刚度包含线性项、立方项和幂函数项,呈现渐软-渐硬特性,等效阻尼比随幅值增大而先增大后减小。数值仿真采用基于谐波平衡法的近似解析方法和基于龙格库塔法的数值方法,揭示了立方刚度对系统的固有频率偏移特性的影响,在一定激励幅值范围内立方刚度可以消除滞回引起的跳跃现象,也揭示了模型参数对系统刚度和阻尼的影响规律。

A wire rope based vibration isolation system is a typical nonlinear passive vibration isolation system.Energy is transferred and dissipated through elastic deformation and inner friction.Based on a wire rope structure with both ends constrained,a nonlinear vibration isolation system with high-order stiffness and hysteretic damping was constructed.The Bouc-Wen model was adopted to characterize the hysteretic restoring force and a dynamic model was established for the system under harmonic displacement excitation.Expressions for equivalent stiffness and equivalent damping ratio were deducted.The equivalent stiffness includes linear,cubic and power function terms,and the system exhibits a softening-hardening characteristics.The equivalent damping ratio increases first and then decreases with vibration amplitude.The harmonic balance method based approximate analytical solution and the 4th-order Runge-Kutta method based numerical solution were adopted in numerical simulation.The results demonstrate that cubic stiffness has an effect on the resonant frequency varying characteristics and can eliminate the jump phenomena in a specific excitation amplitude range.The simulation results also reveal the influences of model parameters on system stiffness and damping.