Nonlinear frequency response analysis and dynamics design of a solid and liquid mixture nonlinear vibration isolator

The solid and liquid mixture (SALiM) vibration isolator is a relatively new passive vibration control technology, especially for the vibration isolation of heavy equipment with low frequency. The isolator contains liquid and elastic solid elements as working media, and its axial stiffness property approximates to bilinear stiffness in certain ranges. This paper focuses on the dynamics design of the isolator and the theoretical analysis of its nonlinear frequency response function (NFRF). The nonlinear dynamic model of a vibration system with a SALiM isolator, i.e. the equation of motion (EOM), is at first established. Then the average method, a classical analytical tool, is employed to estimate the approximate solution of the nonlinear EOM. However, the symmetrical first-order solution obtained with the above method may not be adequate due to the asymmetry of the stiffness of the SALiM isolator. Therefore, the modified average method with a trial expression including a direct current term is introduced. In order to verify the approximate results, a numerical reference based on the Runge-Kutta method is provided for comparison. Moreover, from plots of the resulted NFRFs, it is found that there exists a jump phenomenon induced by bilinearity, which may have harmful impacts on the equipment which is supposed to be protected from vibrations and shocks. To avoid the downside of the bilinear stiffness, the NFRF is analyzed, which allows the determination of the critical values of the isolator parameters to avoid the jump points.