液固混合介质隔振系统的主共振分析

Primary Resonance Analysis of Solid and Liquid Mixture Vibration Isolation System

研究一类具有分段线性—非线性非光滑特性液固混合介质隔振器的主共振解析解。采用摄动法求解非线性段的瞬态响应,由常微分方程理论给出了线性段的瞬态响应。根据响应的连续性与周期性条件,联合接缝法与摄动法分析周期激励作用下系统的主共振响应。而后基于弹性恢复力的傅里叶展开,给出谐波平衡法求解非光滑隔振系统响应的一般步骤,并得到了一阶和二阶近似解。采用龙格—库塔算法对解析方法的有效性进行验证,结果表明:接缝法和数值计算的结果较为吻合,而谐波平衡法的二阶近似比一阶近似解更为精确。

Solid and liquid mixture isolator （SALiM） is a novel isolator which mainly consists of corrugated-pipe type container and elastic element with corrugated-pipe structure. And the stiffness of the isolator is non-smooth because of its piecewise linear-nonlinearity. The instantaneous response for nonlinear piece is difficult to be estimated through using match method to analyze primary resonance response for the system under periodic excitation. In order to obtain the response for nonlinear motion, matching method combined with perturbation method is discussed. In addition, harmonic balance method is combined with Fourier expansion to investigate the problem. In order to validate the above methods including matching method combined with perturbation method and harmonic balance method based on Fourier expansion, the comparison between the results from the different analytic methods and that from Runger-Kutta scheme is given. As a result, it follows that the first analytic method is more satisfying than harmonic balance method. And for harmonic balance method, the second-order result obviously gives higher precision than the lower order does.