Nonlinear analysis of a bio-inspired vertically asymmetric isolation system under different structural constraints

Inspired by the limb configuration of animals in their jumping and landing motions, a systematic investigation on the properties of a class of bio-inspired vertically asymmetric X-shaped (vaX) structures is carried out to explore the advantage of nonlinear characteristics in practical engineering. The nonlinear properties of two different vaX structures are studied under different constraint conditions. Formulations of the nonlinear vibration frequency and absolute displacement transmissibility of the structures are derived by the method of multiple scales. Considering practical conditions, three different constraints (i.e., (a) the same isolations height and assembling angle; (b) the same total rod length and assembling angle; (c) the same total rod length and isolation height) are summarized in this manuscript. Under these conditions, nonlinear properties including nonlinear vibration frequency, isolation performance and static stiffness are systematically discussed. Furthermore, the influences of the assembling pattern (i.e., normal and reverse assembling) on the isolation performance are investigated in detail. The results reveal that there exists rod-length ratio $$s_{1}$$ such that the nonlinear frequency ratio of the vaX-I vibration system is lowest; the natural frequency of the vaX-I structure is independent of the assembling pattern; however, compared with the normally assembled vaX-I structure, a lower resonant peak of the transmissibility can be obtained for the reverse-assembled structure, which suggests that the nonlinear damping of the vaX-I structure is affected by the assembling pattern. Experiments are carried out to verify the influence of the assembling pattern on the natural frequency and isolation performance of the vaX structures.