Transfer Matrix Method for Multibody Systems

2Transfer Matrix Method for Linear Multibody Systems

2.1 Introduction

Strictly speaking, various engineering mechanism systems, such as machine tools, weaponry, carrier rockets, airplanes and vehicles as well as electromechanical systems with controllers, are nonlinear and time‐variant multi‐flexible‐body systems (MFSs). However, the accuracy could also be achieved in many situations even if a linear model of a multi‐rigid‐flexible‐body system is used for an engineering project as then it becomes easy to solve actual engineering problems. The dynamics model of linear MRFSs has therefore become one of the most popular, most important and most practical physical models in engineering fields such as weaponry, shipping, aeronautics, astronautics, communications, general machineries etc. The problems of linear multibody system dynamics (MSD) that are of interest to scientists and engineers include eigenvalue problems, vibration characteristics, steady‐state responses, the orthogonality of eigenvectors and the dynamic responses of linear multibody systems (MSs).

Vibration characteristics are one of the most important dynamics characteristics of mechanical systems. It is hard to obtain justifiable dynamic performance of the mechanical system if the vibration characteristics cannot be solved or pre‐estimated exactly when designing it. It is therefore very important to express exactly the vibration characteristics of MRFSs. For example, it has been shown by theory and experiment ...