On vibration transmission between interactive oscillators with nonlinear coupling interface

Abstract This paper investigates the dynamic characteristics and vibration transmission behaviour of interactive oscillators with nonlinearities at their coupling interface. Three different types of stiffness nonlinearities, i.e., hardening stiffness, softening stiffness and double-well potential type stiffness and cubic damping nonlinearity are considered. Both analytical approximations based on the method of averaging and also numerical integrations are employed to obtain the steady-state response and to determine the vibration transmission level. The time-averaged vibration power variables and kinetic energies of the system and the force transmissibility are formulated and obtained analytically and numerically. Time-averaged transmitted power is used as an index to quantify vibration transmission associated with both periodic responses and non-periodic responses such as chaos. It is found that hardening stiffness nonlinearity at the interface can lead to higher vibration power transmission at high excitation frequencies. In comparison, softening stiffness nonlinearity at the coupling interface can result in higher vibration transmission at lower excitation frequencies. It is shown that the interface with double-well potential stiffness nonlinearity may yield chaotic responses that can significantly affect vibration transmission as indicated by time-averaged transmitted power. It is also found that cubic damping nonlinearity may cause lower time-averaged transmitted and dissipated powers at the interface in the vicinity of resonant frequency. These findings provide better understanding of the effects of nonlinearity at the interface on vibration transmission, and facilitate better designs of coupling interface for control of vibration transmission.