Abstract: 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.

Key words: Harmonic balance method, Match method, Piecewise smooth, Principal resonance, Vibration isolation