Buch, Englisch, 639 Seiten, Format (B × H): 155 mm x 234 mm, Gewicht: 1089 g
ISBN: 978-1-84821-077-6
Verlag: Wiley
Over the last 50 years, the various available methods of investigating dynamic properties of materials have resulted in significant advances in this area of materials science. Dynamic tests have also recently proven to be as efficient as static tests, and have the advantage that they are often easier to use at lower frequency. This book explores dynamic testing, the methods used, and the experiments performed, placing a particular emphasis on the context of bounded medium elastodynamics.
The book initially focuses on the complements of continuum mechanics before moving on to the various types of rod vibrations: extensional, bending and torsional. In addition, chapters contain practical examples alongside theoretical discussion to facilitate the reader's understanding. The results presented are the culmination of over 30 years of research by the authors and will be of great interest to anyone involved in this field.
Autoren/Hrsg.
Fachgebiete
Weitere Infos & Material
Preface xix
Acknowledgements xxix
Part A Constitutive Equations of Materials 1
Chapter 1 Elements of Anisotropic Elasticity and Complements on Previsional Calculations 3
Yvon CHEVALIER
1.1 Constitutive equations in a linear elastic regime 4
1.2 Technical elastic moduli 7
1.3 Real materials with special symmetries 10
1.4 Relationship between compliance Sij and stiffness Cij for orthotropic materials 23
1.5 Useful inequalities between elastic moduli 24
1.6 Transformation of reference axes is necessary in many circumstances 27
1.7 Invariants and their applications in the evaluation of elastic constants 28
1.8 Plane elasticity 35
1.9 Elastic previsional calculations for anisotropic composite materials 38
1.10 Bibliography 51
1.11 Appendix 52
Appendix 1.A Overview on methods used in previsional calculation of fiber-reinforced composite materials 52
Chapter 2 Elements of Linear Viscoelasticity 57
Yvon CHEVALIER
2.1 Time delay between sinusoidal stress and strain 59
2.2 Creep and relaxation tests 60
2.3 Mathematical formulation of linear viscoelasticity 63
2.4 Generalization of creep and relaxation functions to tridimensional constitutive equations 71
2.5 Principle of correspondence and Carson-Laplace transform for transient viscoelastic problems 74
2.6 Correspondence principle and the solution of the harmonic viscoelastic system 82
2.7 Inter-relationship between harmonic and transient regimes 83
2.8 Modeling of creep and relaxation functions: example 87
2.9 Conclusion 100
2.10 Bibliography 100
Chapter 3 Two Useful Topics in Applied Viscoelasticity: Constitutive Equations for Viscoelastic Materials 103
Yvon CHEVALIER and Jean Tuong VINH
3.1 Williams-Landel-Ferry’s method 104
3.2 Viscoelastic time function obtained directly from a closed-form expression of complex modulus or complex compliance 112
3.3 Concluding remarks 136
3.4 Bibliography 137
3.5 Appendices 139
Appendix 3.A Inversion of Laplace transform 139
Appendix 3.B Sutton’s method for long time response 143
Chapter 4 Formulation of Equations of Motion and Overview of their Solutions by Various Methods 145
Jean Tuong VINH
4.1 D’Alembert’s principle 146
4.2 Lagrange’s equation 149
4.3 Hamilton’s principle 157
4.4 Practical considerations concerning the choice of equations of motion and related solutions 159
4.5 Three-, two- or one-dimensional equations of motion? 162
4.6 Closed-form solutions to equations of motion 163
4.7 Bibliography 164
4.8 Appendices 165
Appendix 4.A Equations of motion in elastic medium deduced from Love’s variational principle 165
Appendix 4.B Lagrange’s equations of motion deduced from Hamilton’s principle 167
Part B Rod Vibrations 173
Chapter 5 Torsional Vibration of Rods 175
Yvon CHEVALIER, Michel NUGUES and James ONOBIONO
5.1 Introduction 175
5.1.1 Short bibliography of the torsion problem 176
5.1.2 Survey of solving methods for torsion problems 176
5.1.3 Extension of equations of motion to a larger frequency range 179
5.2 Static torsion of an anisotropic beam with rectangular section without bending – Saint Venant, Lekhnitskii’s formulation 180
5.3 Torsional vibration of a rod with finite length 199
5.4 Simplified boundary conditions associated with higher approximation equations of motion [5.49] 204
5.5 Higher approximation equations of motion 205
5.6 Extension of Engström’s theory to the anisotropic theory of dynamic torsion of a rod with rectangular cross-section 207
5.7 Equations of motion 212
5.8 Torsion wave dispersion 215
5.9 Presentation of dispersion curves 219
5.10 Torsion vibrations
