A State Space Method for Modal Identification of Mechanical Systems from Time Domain Responses

Xiaobo Liu

doi:10.1155/2005/526251

Abstract

A new state space method is presented for modal identification of a mechanical system from its time domain impulse or initial condition responses. A key step in this method is the identification of the characteristic polynomial coefficients of an adjoint system. Once these coefficients are determined, a canonical state space realization of the adjoint system and the system's modal parameters are formulated straightforwardly. This method is conceptually and mathematically simple and is easy to be implemented. Detailed mathematical treatments are demonstrated and numerical examples are provided to illustrate the use and effectiveness of the method.

Highlights

Modal identification is a process to obtain the modal parameters of a mechanical system from measured data
The differences in the methods lie in the measurement databases being used, and the mathematical models being employed for data fitting
We will first consider the case with impulse responses, and extend the method to cover the case with initial condition responses

Summary

Introduction

Modal identification is a process to obtain the modal parameters of a mechanical system from measured data. Each method starts with a system with its physics being governed by linear second order dynamic equations, it seeks to fit the measurement data into a mathematical model, and derives the desired modal parameters from the identified mathematical model. The differences in the methods lie in the measurement databases being used, and the mathematical models being employed for data fitting. We present a new state space method for modal identification. Compared to the existing methods, the main advantage of the new method is in its conceptual and mathematical simplicities In this method, the identification of a dynamic system is first translated into the identification of an adjoint system. The method determines the order and the characteristic polynomial coefficients of the adjoint system Once these coefficients are determined, the state space matrices and the modal parameters are formulated in a straightforward fashion. A couple of examples are provided to illustrate its use and effectiveness

Dynamic equations

Modal identification from impulse responses

Modal identification from initial condition responses

Numerical examples

Conclusions