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Informationen zum Autor Yvon Chevalier is Emeritus Professor at the Institut Superieur de Mécanique de Paris (SUPMECA), France. Since 2000 he has been co-editor in chief Mecanique et Industries journal, supported by the French Association of Mechanics. He is a well-known expert in the dynamics of composite materials and propagation of waves in heterogeneous materials. He also has great experience in the areas of hyper-elasticity and non-linear viscoelasticity of rubber materials. Jean Tuong Vinh is Emeritus University Professor of Mechanical Engineering at the University of Paris VI in France. He carries out research into theoretical viscoelasticity, non-linear functional Volterra series, computer algorithms in signal processing, frequency Hilbert transform, special impact testing, wave dispersion on rods and continuous elements and solution of related inverse problems. Klappentext Dynamic tests have proven to be as efficient as static tests and are often easier to use at lower frequency. Over the last 50 years, the methods of investigating dynamic properties have resulted in significant advances. This book explores dynamic testing, the methods used, and the experiments performed, placing a particular emphasis on the context of bounded medium elastodynamics. The discussion is divided into four parts. Part A focuses on the complements of continuum mechanics. Part B concerns the various types of rod vibrations: extensional, bending, and torsional. Part C is devoted to mechanical and electronic instrumentation, and guidelines for which experimental set-up should be used are given. Part D concentrates on experiments and experimental interpretations of elastic or viscolelastic moduli. In addition, several 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 as such will be of great interest to anyone involved in this field. Zusammenfassung * Dispersion is the phenomenon in which the phase velocity of awave depends on its frequency * Dynamic tests have proven to be as efficient as static testsand are often easier to use at lower frequency. Over the last 50years, the methods of investigating dynamic properties haveresulted in significant advances. Inhaltsverzeichnis 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 Int...
