Dynamics and performance evaluation of an asymmetric nonlinear vibration isolation mechanism

In this work, the dynamics and performance of a harmonically excited asymmetric nonlinear vibration isolation mechanism is investigated using the multi harmonic balance method (MHBM). Asymmetry in the system is introduced in the form of a constant load along with the harmonic excitation. Instead of a truncated cubic nonlinear system considered in the previous works, the fully nonlinear system without any approximation is considered in this study. The MHBM framework considered in this paper is a systematic and computationally efficient method to generate periodic solutions of any order, continue their branches, identify stable, and unstable branches along with the types of bifurcations. Dynamics of the system is investigated with forcing frequency and forcing amplitude as the parameters. With an increase in the value of the constant load, the response diagram shows double folding with softening and hardening behavior and multiple jumps, disappearance of certain types of bifurcations, loss of stability of the periodic solutions, existence of higher order periodic solutions, and chaotic solutions. The transmissibility plots in the presence of the constant load show substantial deterioration in the vibration isolation capability of the isolation system. A comparison of the fully nonlinear system and the truncated cubic system is performed at the end to show that the solutions are qualitatively same but quantitatively different which is an important aspect in practical applications of isolation systems.