Data-driven modeling and analysis of nonlinear isolated mechanical system

Abstract

This study aims to identify nonlinearities in the stiffness and damping characteristics of a passive pneumatic isolator connected to an ultra-precision manufacturing prototype in the uncoupled transverse and horizontal directions. Experimental data are collected using sine sweep tests and is used to plot nonlinear frequency response functions. The resulting analysis reveals a quadratic polynomial relationship between the equivalent stiffness and the system’s dynamic response, indicating a combination of quadratic and cubic nonlinearity. Similarly, the nonlinear damping characteristic is determined using the half-power bandwidth method, which exhibits a quadratic polynomial relationship between the equivalent damping and dynamic response. The linear stability analysis of the system for the identified nonlinear stiffness and damping characteristics reveals that the system remains linearly stable for the given range of frequency and excitation amplitudes. Furthermore, bifurcation analysis reveals the existence of complex solutions, such as period-2 and period-4 solutions, for higher excitation amplitudes.