An Investigation into the Dynamic Interaction Between an Electro-dynamic Shaker and a Test Structure with Cubic Nonlinearity

Abstract

This chapter describes the dynamic behaviour of a coupled system where a nonlinear oscillator is attached and driven harmonically by an electro-dynamic shaker. The shaker is modelled as a linear single degree-of-freedom oscillator and the nonlinear attachment is modelled as a hardening Duffing oscillator. The attachment consists of four elastic wires, represented as springs, and its nonlinearity is due to the geometric configuration of the springs, which incline as they extend. The mass of the nonlinear system is much less than the moving mass of the shaker so that the nonlinear system has little effect on the shaker dynamics. The objective is to explore the dynamic behaviour of this system under a range of different conditions. Of particular interest is the situation when the linear natural frequency of the nonlinear system is less than the natural frequency of the shaker such that the frequency response curve of the nonlinear system bends to higher frequencies and thus interacts with the resonance frequency of the shaker. It is found that for some values of the system parameters a two-part frequency response curve can occur: a closed detached curve can appear as a part of the overall amplitude-frequency response, and this detached curve can lie outside or inside the main continuous resonance curve.