多自由度非线性隔振系统建模及其非共振响应

DYNAMIC MODELING FOR MULTI-DEGREE-OF-FREEDOM NONLINEAR VIBRATION ISOLATION SYSTEM AND ITS NONRESONANT RESPONSE

非线性因素会对系统解耦产生影响,因此工程实际中的非线性隔振系统一般为多自由度系统,同时,船舶机械隔振系统的基座应视为具有一定机械阻抗的弹性体。基于上述考虑,对船舶机械非线性隔振系统进行了建模,并特别讨论了非线性项的表达式。通过分析非线性因素与系统解耦之间的关系,使得系统得以简化的同时,保留了系统主要的动力学特性。还应用多尺度法对该类型非线性隔振系统在其主要工作状态——非共振状态下的动态响应进行了分析,并通过数值计算验证了多尺度法得出的一阶近似解的有效性以及非线性因素对系统的影响。

Nonlinear vibration isolation system used practically is generally a multi-degree-of-freedom system due to effect of nonlinearity on decoupling of system.Furthermore,the base of an on-board machine cannot be assumed as a rigid body but an elastic one with certain mechanical impedance.According to these,the dynamic equations of the nonlinear vibration isolation system for the on-board machine are established and the expressions of the nonlinear iterms are discussed especially.By analyzing the relationship between decoupling and the nonlinear factors,the system is simplified to a 4-degree-of-freedom system and its primary dynamic characteristics are retained.The method of multiple scales is used to analyze the dynamic response of the system in its nonresonant state and the numerical simulation is carried out to confirm the validity of the results obtained by using the method of multiple scales and the effects of the nonlinear factors.