非线性阻尼非线性刚度隔振系统随机动力学特性研究

针对随机激励环境，同时引入刚度和阻尼非线性来提高隔振系统的隔振性能.刚度和阻尼非线性分别是由水平弹簧和水平阻尼的几何布置获得.通过求解Fokker-Planck-Kolmogorov(FPK)方程等效非线性随机振动方程来研究非线性隔振系统在随机激励下的隔振性能，并使用路径积分和Monte-Carlo数值方法进行验证.在此基础上研究刚度非线性和阻尼非线性对隔振系统在随机激励下力传递率及其概率分布的影响.研究表明随着噪声强度的增加，非线性阻尼抑制振动的能力增强，但是在较小的随机激励下线性阻尼优于非线性阻尼.

An Investigation on Nonlinear-Damping and Nonlinear-Stiffness Vibration Isolation Systems Under Random Excitations

Both nonlinear damping and nonlinear stiffness were introduced in vibration isolation systems under random excitations to improve the isolation performance.The nonlinear damping and nonlinear stiffness were realized through the geometric arrangement of the horizontal springs and horizontal dampers.The performance of the nonlinear vibration isolator under random excitation was evaluated with the equivalent Fokker-Planck-Kolmogorov (FPK) equation transformed by the nonlinear stochastic vibration equation.The effects of the nonlinearity introduced in stiffness and damping on the transmissibility and its probability were studied.It is found that,for high levels of random excitations,the damping nonlinearity brings larger reduction of the random vibration response,and the gap between the linear and the nonlinear dampings is enlarged;however,for low levels of random excitations,the nonlinear damping has less efficacy than the linear damping.