8 Computer Analysis of Flexibly Supported Multibody Systems Ibrahim Esat

Back

Brunel University

M. Dabestani Furlong Research Foundation

8.1 Introduction ........................................................................ 8-1

8.2 Theory ................................................................................... 8-2

Definitions and Assumptions † Equations of Motion for

the Linear Model † Linear Momentum – Force

Systems † Generalization of the Equations of Moment

of Momentum † Assembly of Equations

8.3 A Numerical Example ........................................................ 8-7

A Uniform Rectangular Prism † VIBRATIO Output

8.4 An Industrial Vibration Design Problem ......................... 8-11

Static Deflection † Natural Frequencies † Transient

Response Analysis † Frequency Analysis † A Flexibly

Supported Engine — A Numerical Problem

8.5 Programming Considerations ........................................... 8-16

8.6 VIBRATIO ........................................................................... 8-17

Capabilities † Modeling on VIBRATIO

8.7 Analysis ................................................................................ 8-24

Analysis Options † Eigenvalue Analysis † Linear

Deflection Analysis † Frequency Analysis †

Time-Domain Analysis

8.8 Comments ........................................................................... 8-31

Appendix 8A VIBRATIO Output for Numerical

Example in Section 8.3 ........................................................ 8-32

Summary

This chapter presents the Euler– Newton formulation of oscillatory behavior of a multibody system interconnected

by discrete stiffness elements. Bodies are interconnected by springs, and/or dashpots (dampers). Connections are

described in terms of end coordinates of springs relative to the coordinate system of the body to which it is attached.

Stiffness characteristics are described along the three principal axes of springs. Orientation of springs and masses are

described by using appropriate Euler angles. The model developed is linear, and gyroscopic influences are ignored.

The chapter gives a detailed treatment of rigid bodies in three dimensional space using vector-matrix formulation.

Complete formulation and assembly issues relating to programming aspects are presented. A software suite called

VIBRATIO, based on the present formulation, is described. The capabilities of VIBRATIO are indicated and

illustrative examples are given in both frequency and time domains. A student version of VIBRATIO is available at

no cost to the users of this handbook at www.signal-research.com.

Навигация