8.1 Introduction

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There are many commercial software packages for analysis of kinematics and dynamics of multibody

linkage systems. There are fewer software tools for analysis of vibration of multiple rigid-body systems

8-1

© 2005 by Taylor & Francis Group, LLC

in 3-D space, even though some finite element

analysis (FEA) packages offer rigid-body capability.

Common FEA software packages treat rigid

bodies using point masses or point inertias.

Although this is not a serious restriction, when

it comes to attaching discrete stiffness elements to

a body away from its center of gravity (COG), the

attachment is achieved by introducing “lever

arms” with a very high Young’s modulus. One

may argue that the error introduced in doing so is

acceptable but how true this argument is depends on the problem, and there is no escape from the fact

that this approach can create ill-conditioned stiffness matrices. The correct way, however, is to

incorporate the created kinematic constraints into rigid-body geometries. This is the approach

presented in this chapter. A typical rigid multibody system supported or interconnected by discrete

spring elements, as considered here, is shown in Figure 8.1. The chapter presents a

complete formulation of a multibody system flexibly supported by linear mountings. The formulations

and methods proposed in this chapter are used in the VIBRATIO suite of vibration analysis

software.

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