Transfer Matrix Method for Multibody Systems

6Transfer Matrix Method for Multi‐flexible‐body Systems

6.1 Introduction

The transfer matrix method for multi‐rigid‐body systems was introduced in Chapter 5. The translational and angular accelerations together with internal forces and moments are taken as new state variables instead of position coordinates in the original transfer matrix method for multibody systems (MSTMM). This results in totally different transfer matrices of elements and algorithms compared with the original MSTMM. The proposed method expands the advantages of the MSTMM by allowing more sophisticated numerical integration procedures to be used, such as the Runge–Kutta method: no global dynamics equations of the system are required, matrices have low order, setup of the global transfer equation is highly programmable, and solution allows high computational precision since linearization is not required anymore. The new method is simple, straightforward, efficient, practical and provides a powerful tool for multibody system dynamics (MSD).

The dynamics of a multi‐rigid‐flexible‐body system could also be solved by the transfer matrix method, in a way that is similar to dealing with a multi‐rigid‐body system. Hereafter, the way to study the dynamics of a multi‐rigid‐flexible‐body system by using the transfer matrix method is called the transfer matrix method for multi‐flexible‐body systems, which is introduced in this chapter.

The floating frame of reference formulation is used while modeling a flexible body, ...