This book focuses on basic and advanced concepts of wave propagation in diverse material systems and structures. Topics are organized in increasing order of complexity for better appreciation of the subject. Additionally, the book provides basic guidelines to design many of the futuristic materials and devices for varied applications. The material in the book also can be used for designing safer and more lightweight structures such as aircraft, bridges, and mechanical and structural components. The main objective of this book is to bring both the introductory and the advanced topics of wave propagation into one text. Such a text is necessary considering the multi-disciplinary nature of the subject. This book is written in a step-by step modular approach wherein the chapters are organized so that the complexity in the subject is slowly introduced with increasing chapter numbers. Text starts by introducing all the fundamental aspects of wave propagations and then moves on to advanced topics on the subject. Every chapter is provided with a number of numerical examples of increasing complexity to bring out the concepts clearly The solution of wave propagation is computationally very intensive and hence two different approaches, namely, the Finite Element method and the Spectral Finite method are introduced and have a strong focus on wave propagation. The book is supplemented by an exhaustive list of references at the end of the book for the benefit of readers.
Table of Contents
1. Introduction. Essential Components of a Wave. Need for Wave Propagation Analysis in Structures and Materials. Organization and Scope of the Book. 2. Local and Non Local Elasticity: Introductory Concepts. Introduction to the Theory of Elasticity. Theory of Gradient Elasticity. 3. Introduction to the Theory of Composites and Functionally Graded Materials. Introduction to Composite Material. Theory of laminated Composites. Introduction to Functionally Graded Materials (FGM). 4. Introduction to Integral Transforms. Fourier Transforms. Short-term Fourier Transform (STFT). Wavelet Transforms. Laplace Transforms. Comparative Merits and Demerits of Different Transforms. 5. Introduction to Wave Propagation. Concept of Wavenumber, Group Speeds, and Phase Speeds. Wave Propagation Terminologies. Spectral Analysis of Motion. General Form of Wave Equations and their Characteristics. Different Methods of Computing Wavenumbers and Wave Amplitudes. 6. Wave Propagation in One Dimensional Isotropic Structural Waveguides. Hamilton’s Principle. Wave Propagation in 1D Elementary Waveguides. Wave Propagation in Higher-Order Waveguides. Wave Propagation in Rotating Beams. Wave Propagation in Tapered Waveguides. 7. Wave Propagation in Two Dimensional Isotropic Waveguides. Governing Equations of Motion. Wave Propagation in Thin Plates. 8. Wave Propagation in Laminated Composites. Wave Propagation in a 1D Laminated Composite Waveguide. Wave Propagation in Thick 1D Laminated Composite Waveguides. Wave Propagation in Composite Cylindrical Tubes. Wave Propagation in Two Dimensional Composite Waveguides. Wave Propagation in 2D Laminated Composite Plates. 9. Wave Propagation in Sandwich Structural Waveguides. Wave Propagation in Sandwich Beams Based on Extended Higher Order Sandwich Plate Theory (EHSAPT). Wave Propagation in 2D Sandwich Plate Waveguides. 10. Wave Propagation in Functionally Graded Material Waveguides. Wave Propagation in Lengthwise Graded Rods. Wave Propagation in a Depthwise Graded FGM beam. Wave Propagation on Lengthwise Graded Beam. Wave Propagation in 2D Functionally Graded Structures. Thermo-Elastic Wave Propagation in Functionally Graded Waveguides. 11. Wave Propagation in Nanostructures and Nanocomposite Structures. Introduction to Nanostructures. Wave Propagation in MWCNTS using the Local Euler–Bernoulli Model. Wave Propagation in MWCNT through a Local Shell Model. Wave Propagation in Non-Local Stress Gradient Nanorods. Axial Wave Propagation in Nonlocal Strain Gradient Nanorods. Wave Propagation in Higher Order Nanorods using the ESGT model. Wave Propagation in Nanobeams using ESGT Formulations. Wave Propagation in MWCNT using the ESGT Model. Wave Propagation in Graphene. Wave Propagation in Graphene in an Elastic Medium. Wave Propagation in a CNT-Reinforced Nanocomposite Beam. 12. Finite Element Method for Wave Propagation Problems. Introductory Concepts. Variational Principles. Energy Theorems. Finite Element Formulation: H-Type Formulation. Superconvergent FE Formulation. Time Domain Spectral Finite Element Formulation-A p-Type Finite Element Formulation. Solution Methods for Finite Element Method. Direct Time Integration. Numerical Examples. Modeling Guidelines for Wave Propagation Problems. 13. Spectral Finite Element Formulation. Introduction to Spectral Finite Element. Fourier Transform-Based Spectral Finite Element Formulation. Wavelet Transform–Based Spectral Finite Element Formulation. Laplace Transform–Based Spectral Finite Element Formulation. 14. Wave Propagation in Smart Composite Structures. Introduction. Constitutive Models for Piezoelectric Smart Composite Structures. Constitutive Model for Magnetostrictive Materials. Constitutive Model for Electrostrictive Materials. Wave Propagation in Structures with Piezoelectric and Electrostrictive Actuators . Wave Propagation in a Composite Beam with Embedded Magnetostrictive Patches. 15. Wave Propagation in Defective Waveguides. Wave Propagation in Single Delaminated Composite Beams. Wave Propagation in Beams with Multiple Delaminations. Wave Propagation in a Composite Beam with Fiber Breaks or Vertical Cracks. Wave Propagation in Degraded Composite Structures. Wave Propagation in A 2D Plate with Vertical Cracks. Wave Propagation in Porous Beams. 16. Wave Propagation in Periodic Waveguides. General Considerations on the Repetitive Volume Elements. Theory of Bloch Waves. Spectral Finite Element Model for Periodic Structures. Dispersion Characteristics of a Periodic Waveguide with Defects. Numerical Examples. SFEM for Periodic Structures. 17. Wave Propagation in Uncertain Waveguides. Monte Carlo Simulations in the SFEM Environment. Results and Discussion. 18. Wave Propagation in Hyperelastic Waveguides. Theory of Hyperelasticity. Nonlinear Governing Equation for an Isotropic Rod. Time Domain Finite Element Models for Hyperelastic Analysis. FSFEM for Hyperelastic Wave Propagation. Numerical Results and Discussion. Nonlinear Flexural Wave Propagation in Hyperelastic Timoshenko Beams. 19. Index.
Dr. Srinivasan Gopalakrishnan is a professor in the Department of Aerospace Engineering at the Indian Institute of Science, Bangalore. Professor Gopalakrishnan works in the area of wave propagation in complex mediums, structural health monitoring, and modeling of nanostructures, wherein he has made seminal contributions.
"The book browses rapidly in the first chapters into different aspects of wave propagation in many different materials, considering anisotropy, heterogeneity and higher-order continua. It then deals with a large list of more specific aspects at the forefront of current research. The book will be of interest both to top-level researchers and to students wishing to get of broad view of up-to-date research topics in wave propagation."
— Régis Cottereau, CNRS, CentraleSupélec, Université Paris-Saclay, France
"The book provides a self-contained exposition of elastic wave propagation in material and structures. Besides covering the general background on elastic wave propagation, it covers a wide variety of interesting applications of wave propagation in different types of wave guides and nano structures. There are many interesting chapters covering important applications such as wave propagation in composite structures, nanostructures and in materials including electric and magnetic regions. There is also an interesting chapter on wave propagation in uncertain wave guides using Monte Carlo simulations. Overall, the book can serve as an excellent reference book for both engineers and applied mathematicians."
—Kristian Sandberg, Computational Solutions, Inc.
The main strength in this book is the brief but very effective fundamentals that one must know or recapitulate before understand the harder materials on wave propagation. The breath and deepness in the material covered is quite valuable for graduate students those who will embark on the journey with acoustic or ultrasonic wave propagation. Particularly I like the concept of stitching the wave propagation in classical media, waves in periodic media, wave in micro to nano scale structures and very wide topics but brief fundamentals together in to a one chain."
— Sourav Banerjee, University of South Carolina, USA