How to Analyse the Static and Dynamic Response of Viscoelastic Components

Oyadiji, S O

First Published - August 2004
Softback, 118 Pages

The target audience of this book is a linear static finite element analyst, including an engineering graduate with at least one year’s experience of linear static finite element analysis. The aim is to introduce the static and dynamic structural analyses of viscoelastically-damped structures. These structures consist of viscoelastic materials sandwiched between parts or components made of metallic or composite materials. Viscoelastic materials are widely used for vibration, shock and noise control in the automotive, marine, aerospace, electrical/electronic, defence, instrumentation and home appliance industries.

Linear static and non-linear quasi-static analyses of structures incorporating viscoelastic materials are covered in this booklet. These analyses involve both elastic and hyperelastic material models. Furthermore, the steady-state vibration and shock response (transient vibration) analyses of viscoelastically-damped structures are presented. The theories underpinning these static and dynamic analyses, and the experimental methods for characterising the intrinsic mechanical properties of the materials required for the analyses, are presented.

It should be noted that the book does not include metal plasticity, metal creep and viscoplasticity. Also, only structural response is considered. Therefore, thermal effects such as heat transfer and heat conduction of viscoelastic components are excluded. In addition, electrical, magnetic and electromagnetic effects are also excluded.

Contents

1. Introduction

• Items Covered
• Items not Covered
• Applications of Viscoelastic Materials
• Layout of Booklet

2. Fundamentals of Viscoelasticity

• 2.1 Linear Viscoelasticity
• 2.2 Definitions of Stress Relaxation Modulus and Creep Compliance Function
• 2.3 Definitions of Complex Modulus and Complex Compliance
• 2.4 Constitutive Equations of Viscoelasticity
  • 2.4.1 Integral Formulation of the Constitutive Equation
  • 2.4.2 Differential Formulation of Constitutive Equations Based on Mechanical Models
  • 2.4.3 Generalised Differential Formulation of the Constitutive Equations
  • 2.4.4 Fractional Calculus Formulation of the Constitutive Equations
  • 2.4.5 Formal Relation Between Relaxation and Complex Moduli
• 2.5 Generalised Hooke’s Law and Interconversion of Properties
• 2.6 Hyperelastic Behaviour of Elastomers/Rubbers
  • 2.6.1 Modelling the Behaviour of Solid Elastomers/Rubbers
  • 2.6.2 Modelling Compressibility Effects on Behaviour of Elastomers
  • 2.6.3 Modelling the Behaviour of Elastomeric Foams
• 2.7 Effects of Temperature and Frequency

3 Characterisation of Static and Dynamic Properties of Viscoelastic Materials

• 3.1 Experimental Static Test Methods
  • 3.1.1 Uniaxial Tension and Compression Methods
  • 3.1.2 Equibiaxial Method
  • 3.1.3 Planar and Simple Shear Methods
• 3.2 Experimental Dynamic Test Methods
  • 3.2.1 Choice of Test Method
  • 3.2.2 Creep and Stress Relaxation Methods
  • 3.2.3 Torsion Pendulum Method
  • 3.2.4 Forced Vibration Non-Resonance Methods
  • 3.2.5 Resonance Methods
  • 3.2.6 Wave Propagation Methods
• 3.3 Characterisation of the Complex Moduli of Materials
  • 3.3.1 Illustrative Experimental Procedures
  • 3.3.2 Method of Reduced Variables
  • 3.3.3 Models for Representing Complex Moduli

4 General FEA Procedures/Guidelines

• 4.1 Initial Considerations
• 4.2 Choice of Finite Elements
  • 4.2.1 Linear versus Quadratic Elements
  • 4.2.2 Full versus Reduced Integration
  • 4.2.3 Compressible versus Incompressible Material Behaviour
• 4.3 Choice of Material Models/Properties and Type of Analysis
  • 4.3.1 Instantaneous or Long-term Modulus for Static Elastic Analysis
  • 4.3.2 Hyperelastic Material Models for Static Hyperelastic Analysis
  • 4.3.3 Relaxation Moduli for Time Domain Dynamic Analysis
  • 4.3.4 Complex Moduli for Frequency Domain Dynamic Analysis

5 Examples of Static Analysis of Viscoelastic Components using FEM

• 5.1 Static Stress Distribution in a Cantilevered Lap-Jointed Beam
  • 5.1.1 Geometrical and material properties
  • 5.1.2 Finite element analysis
  • 5.1.3. Discussion of results
• 5.2 Hyperelastic Behaviour of Rubber Mount
  • 5.2.1 Finite element modelling
  • 5.2.2 Discussion of results

6 Examples of Time Domain Dynamic Analysis of Viscoelastic Components using FEM

• 6.1 Transient Response of Mechanical Filters
  • 6.1.1 Derivation of Extensional Relaxation Modulus
  • 6.1.2 Finite Element Model
  • 6.1.3 Discussion of Results
• 6.2 Shock Loading of Rubber Mounts
  • 6.2.1 Derivation of Prony Series Constants
  • 6.2.2 Finite Element Model
  • 6.2.3 Discussion of Results

7 Examples of Frequency Domain Analysis of Viscoelastic Components using FEM

• 7.1 Vibration Transmissibility of Rubber Isolators
  • 7.2.1 Finite Element Modelling
  • 7.2.2 Predicted and Measured Characteristics
• 7.2 Vibration Characteristics of Potted Beam and Plate
  • 7.2.1 Finite Element Analysis
  • 7.2.2 Discussion of Results

8 Concluding Remarks

9 References

Appendix: Description of ABAQUS FEA Elements Used in Examples

Glossary of Terms