Nonlinear Normal Modes for Multi-Degree-of-Freedom Nonlinear Vibration Isolation System

Abstract

Nonlinear vibration isolation system (VIS) plays an important role for improving the capability of hydroacoustic stealth of naval vessels. In engineering, Nonlinear VIS is generally a multi-degree-of-freedom system and its mathematical model is a set of coupled differential equations. Nonlinear normal mode (NNM) is an effective tool for decoupling and analyzing the dynamics of this coupled system. In this paper, taking the flexibility of the base into consideration, the equations of motion of an on-board VIS with quadric and cubic nonlinearities is formulated. The NNMs of this multi-degree-of-freedom nonlinear VIS are constructed by using the invariant manifold approach. The invariant surfaces of the NNMs and the decoupled oscillators are presented.