被动隔振体非线性振动的能量迭代解法

研究了由基础振动激励、弹性材料隔离的被动隔振体的强非线性动力响应。用变形的三次多项式函数表征隔振材料的非线性刚度特性,建立了被动隔振体的非线性动力学方程,得到有阻尼受迫振动Duffing方程。将求解强非线性自治系统的能量迭代方法加以改进,推广应用到强非线性非自治系统,求出周期响应的近似解析解表达式,以及幅频关系、相频关系和隔振系数的近似表达式。算例中应用本方法与Runge-Kutta方法进行了对照,结果表明求解精度较高。本文利用计算机进行了辅助推导。

Energy-iteration Method for Nonlinear Oscillation of a Passively Vibration-isolated Body

Seismic responses of the body isolated by resilient material with strongly nonlinear stiffness are investigated.The nonlinear stiffness characteristics of the vibration isolating material are described by a cubic polynomial function of the deformation.The nonlinear dynamic equation is developed as a forced damping Duffing equation.The energy-iteration method for strongly nonlinear autonomous system is modified and then adopted to solove this non-autonomous problem with strong nonlinearity.The approximate analytic expression of periodic response is derived,the relationships between amplitude-frequency and phase-frequency,and coefficient of vibration isolating are also obtained. Compared with the result from Runge-Kutta method,the example confirms the accuracy of the proposed method.