Displacement transmissibility evaluation of vibration isolation system employing nonlinear-damping and nonlinear-stiffness elements

Undesired oscillations commonly encountered in engineering practice can be harmful to structures and machinery. Vibration isolation systems are used to attenuate undesired oscillations. Recently, there has been growing interest in nonlinear approaches towards vibration isolation systems design. This work is focused on investigating the effect of nonlinear cubic viscous damping in a vibration isolation system consisting of a magnetic spring with a positive nonlinear stiffness, and a mechanical oblique spring with geometric nonlinear negative stiffness. Dynamic model of the vibration isolation system is obtained and the harmonic balance method (HBM) is used to solve the governing dynamic equation. Additionally, fourth order Runge–Kutta numerical simulation is used to obtain displacement transmissibility of the system under investigation. Results obtained from numerical simulation are in good agreement with those obtained using HBM. Results show that introducing nonlinear damping improves the performance of the vibration isolation system. Nonlinear damping purposefully introduced into the described vibration isolation system appears to eliminate undesired frequency jump phenomena traditionally encountered in quasi-zero-stiffness vibration isolation systems. Compared to its rival linear vibration isolation system, the described nonlinear system transmits less vibrations around resonant peak. At lower frequencies, both nonlinear and linear isolation systems show comparable transmissibility characteristics.