含立方刚度和滞回的隔振系统动力学特性分析

DYNAMIC CHARACTERISTICS OF VIBRATION ISOLATION SYSTEM WITH CUBIC STIFFNESS AND HYSTERESIS

包含立方刚度和Bouc–Wen型滞回的隔振系统具有复杂的非线性动力学特性。系统无阻尼响应模型可基于无滞回恢复力建立,利用谐波平衡法和泰勒展开求得近似解析解。系统有阻尼响应模型可利用解析/数值联合方法求解,该方法基于谐波平衡法和Levenberg–Marquardt迭代算法,对于滞回产生的多值非光滑函数项,先计算时域响应再通过快速傅里叶变换求解谐波项系数。上述方法在含水平绞制梁的非线性隔振系统分析中得到有效应用。分析表明,在Bouc–Wen型滞回和立方刚度的综合影响下,隔振系统呈现渐软-渐硬特性,滞回阻尼和线性阻尼都可以有效抑制共振,但前者高频隔振效果优于后者。

The vibration isolation system with cubic stiffness and Bouc–Wen type hysteresis shows complex nonlinear dynamic characteristics.An undamped response model is established based on an anhysteretic restoring force.An approximate analytical solution is derived by the harmonic balance method(HBM)and the Taylor expansion.An analytical/numerical method is proposed to calculate the damped response of the vibration isolation system,based on the HBM and Levenberg–Marquardt algorithm.For the multi-value non-smooth function terms,the harmonic term coefficients are obtained by applying the fast Fourier Transform for the calculated time-domain response.The proposed methods are applied to a nonlinear vibration isolation system with horizontal wire ropes.It is verified that the vibration isolation system has a softening-hardening stiffness with cubic stiffness and Bouc–Wen type hysteresis.Both hysteretic damping and linear damping can effectively suppress the resonance,while with the hysteretic damping,better vibration isolation performance is shown at high frequencies.