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Role Of Damping In Finite Elements


Role Of Damping In Finite Elements











This report examines the role of damping in Finite Element analysis and is intended as a review of methods available as a guide to how they should be effectively employed.

It was prepared under the guidance of the NAFEMS Dynamics Working Group. Thanks are due to the past and present members of that group and the member companies, which they represent for the voluntary effort, which is essential to the work of NAFEMS and the usefulness of this report.

Contents

Preface

Nomenclature

Part 1 - The Significance of Damping in Structural Response

1.1 Resonant response

1.2 Transient Response

1.3 Problems arising from resonant

1.4 Nature of Damping

1.4.1 Material Damping

1.4.2 Damping due to Mechanical Construction

1.5 Damping Models

1.5.1 Viscous Damping

1.5.2 Hysteretic Damping

1.5.3 Coulomb Damping

1.5.4 Advanced Models

Part 2 - The Measurement of Damping

2.1 Introduction

2.2 Evaluation of Damping

2.2.1 Free Vibration Decay

2.2.2 Resonant Amplitude

2.2.3 Half-Power (Bandwidth) Method

2.2.4 Energy Loss Per Cycle (Resonance Testing)

2.2.5 Nyquist Diagram

(a) Viscous Damping
(b) Hysteretic Damping
(c) Improved Damping Estimates

2.2.6 Inverse Method

2.2.7 Evaluation of Damping in Real Structures

(a) Free Decay
(b) Curve Fitting Techniques

2.2.8 Comparison of Damping Measurements

2.3 Experimental Testing - Errors in Damping Estimates

2.3.1Test set-up and Excitation Methods

2.3.2 Measurement of Response Function

(a) Aliasing
(b) Leakage
(c) Windowing
(d) Averaging

2.3.3 Analysis of the Frequency Response Function

(a) FRF Measurement
(b) Error in Frequency Response Functions
(c) Determination of The Damping Value

2.3.4 Structural Non-linearities

Part 3 - The Use of Damping in Finite Element Codes

3.1 Introduction

3.2 Damping Models available in Finite Element Codes
3.2.1 Modela Solution Methods

(a) Rayleigh Damping
(b) Modal Damping
(c) Composite Modal Damping
(d) Hysteretic Damping

3.2.2 Direct Solution Methods

(a) Damping via Material Models
(b) Discrete Dampers
(c) Frequency Dependent Damping

3.3 Relationships between Empirical Models and Material Models

3.4 Relationships between Empirical

3.4.1 Rayleigh Damping

3.4.2  Modal Damping

3.4.3  Composite Modal Damping

3.4.4 Hysteretic Damping

3.4.5 Equivalent Dependent Damping

3.5 Application of Damping Models and Values to Finite Element Analyses


Part 4 - Sensitivity of Finite Element Analyses to Damping

4.1 Introduction

4.2 Model DEscriptions

4.2.1 Deep Simpy-Supported Beam

4.2.2 Simpy-Supported Plate

4.3 Dynamic Analysis Procedures

4.4 Harmonic Excitation

4.4.1 Modal Superposition Method

4.4.2 Direct Solution Method

4.4.3 Model Superposition - Effect of Damping on Response of a Simpy-Supported Beam

4.4.4 Direct Solution - Effect of Damping on Response of a Simpy-Supported Beam

4.4.5 Using Finite Element Analysis Results to Measure Damping

4.4.6 Effect of Damping on Response of a Simpy-Supported plate

4.5 Transient Excitation

4.5.1 Analysis Methods

4.5.2 Definition of Forcing Function

4.5.3 Modal Superposition - Effect of Damping on Response of a Simpy-Supported Beam

4.6 Periodic Excitation

4.7 Random Excitation

4.8 Discussion on the Use of Different Damping Models


Part 5 - Discussion and Conclusions

References

Glossary

Tables

Figures

Appendices


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About

P.W. Spence & C.J. Kenchington

First Published - February 1993

Softback, 140 Pages