7 Vibration Modeling and Software Tools Datong Song

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National Research Council of Canada Cheng Huang

National Research Council of CanadaZhong-Sheng Liu

National Research Council of Canada

7.1 Introduction ....................................................................... 7-1

7.2 Formulation ....................................................................... 7-2

Differential Formulation † Integral Formulation and

Rayleigh – Ritz Discretization † Finite Element

Method † Lumped Mass Matrix † Model Reduction

7.3 Vibration Analysis ............................................................. 7-9

Natural Vibration † Harmonic Response † Transient

Response † Response Spectrum

7.4 Commercial Software Packages ........................................ 7-13

ABAQUS † ADINA † ALGOR † ANSYS †

COSMOSWorks † MSC.Nastran †

ABAQUS/Explicit † DYNA3D † LS-DYNA

7.5 The Basic Procedure of Vibration Analysis ..................... 7-16

Planning † Preprocessing † Solution †

Postprocessing † Engineering Judgment

7.6 An Engineering Case Study .............................................. 7-19

Objectives † Modeling Strategy † Boundary

Conditions † Material † Results

7.7 Comments .......................................................................... 7-21

Summary

In this chapter, several aspects of vibration modeling are addressed. They include the formulation of the

equations of motion both in differential form and integral form, the Rayleigh – Ritz method and the finite

element methods, and model reduction. Natural vibration analysis and response analysis are discussed in detail.

Several commercial finite element analysis (FEA) software tools are listed and their capabilities for vibration

analysis are introduced. The basic procedure in using the commercial FEA software packages for vibration

analysis is outlined (also see Chapter 6 and Chapter 9). The vibration analysis of a gearbox housing is

presented to illustrate the procedure.

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