Displacement Transmissibility of a Four-Parameter Isolator with Geometric Nonlinearity

This study is concerned with structural vibration reduction using a four-parameter isolator designed as a scissor-like structure, which can induce geometric nonlinearity during the deformation process. The displacement transmissibility of the isolator including the geometric nonlinearity under base excitations is thoroughly investigated. First, the dynamic model of the four-parameter isolator is presented. Then, by utilizing the harmonic balanced method (HBM), the steady-state solutions of the inertia mass and auxiliary spring of the proposed isolator are derived. The analytical solutions are validated by comparing with those obtained by the direct numerical integrating method. Besides, the natural frequency of the nonlinear isolation system is presented and investigated. Moreover, the isolation performance of the four-parameter isolator is assessed in terms of the relative and absolute displacement transmissibilities, and compared with that of the linear Zener model, by which the advantages of the present isolator have been clearly revealed. The effects of various design parameters on the displacement transmissibility of the isolator are also analyzed. Finally, a further comparison between the analytical and experimental results under base excitation also shows that the mechanical model used for the four-parameter isolator is accuracy enough. The present results may provide a useful theoretical basis for the design of the four-parameter isolator in engineering practice.