Includes bibliographical references (pages 909-938) and index.

Note continued: 14.2.2. Constitutive Model For Smart Piezo Composites -- 14.3. Constitutive Model For Magnetostrictive Materials -- 14.3.1. Coupled Constitutive Model -- 14.4. Constitutive Model For Electrostrictive Materials -- 14.4.1. Constitutive Relation Using Polarization -- 14.4.2. Quadratic Model -- 14.4.3. Hyperbolic Tangent Constitutive Relations -- 14.5. Wave Propagation In Structures With Piezo-Electric And Electrostrictive Actuators -- 14.5.1. Governing Equation For A Beam With Electrostrictive Actuator -- 14.5.2. Governing Equation For Beam With Piezoelectric Actuator -- 14.5.3. Computation Of Wavenumbers And Group Speeds -- 14.5.4. Spectral Finite Element Formulation -- 14.5.5. Numerical Examples -- 14.6. Wave Propagation In A Composite Beam With Embedded Magnetostrictive Patches -- 14.6.1. Nth-Order Shear Deformation Theory With mth-Order Poisson Lateral Contraction -- 14.6.2. Spectral Analysis -- 14.6.3. Numerical Examples -- 15.1. Wave Propagation In Single Delaminated Composite Beams -- 15.1.1. Numerical Examples -- 15.2. Wave Propagation In Beams With Multiple Delaminations -- 15.2.1. Numerical Example -- 15.3. Wave Propagation In A Composite Beam With Fiber Breaks Or Vertical Cracks -- 15.3.1. Modeling Dynamic Contact Between Crack Surfaces -- 15.3.2. Modeling Of Surface-Breaking Cracks -- 15.3.3. Distributed Constraints At The Interfaces Between Sub-Laminates And Hanging Laminates -- 15.3.4. Numerical Example -- 15.4. Wave Propagation In Degraded Composite Structures -- 15.4.1. Empirical Degraded Model -- 15.4.2. Average Degradation Model -- 15.4.3. Numerical Example -- 15.5. Wave Propagation In A 2D Plate With Vertical Cracks -- 15.5.1. Flexibility Along The Crack -- 15.6. Wave Propagation In Porous Beams -- 15.6.1. Modified Rule Of Mixtures -- 15.6.2. Numerical Results -- 16.1. General Considerations On The Repetitive Volume Elements -- 16.2. Theory Of Bloch Waves -- 16.3. Spectral Finite Element Model For Periodic Structures -- 16.3.1. Spectral Super Element Approach -- 16.3.2. Efficient Computation Of [KSS] -- 16.4. Dispersion Characteristics Of A Periodic Wave-Guide With Defects -- 16.4.1. Determinantal Equation Approach -- 16.4.2. Transfer Matrix Eigenvalue Approach -- 16.5. Numerical Examples -- 16.5.1. Beam With Periodic Cracks -- 16.6. SFEM For Periodic Structures -- 16.6.1. Wave Propagation Analysis -- 16.6.2. Comparison Of Computational Efficiency Of Periodic SFEM Model As Opposed To FEM -- 17.1. Monte Carlo Simulations In The SFEM Environment -- 17.2. Results And Discussion -- 17.2.1. Effect Of Uncertainty On Velocity Time Histories -- 17.2.2. Comparison Of Computational Efficiency Of FEM And SFEM Under MCS -- 17.2.3. Distribution Of Time Of Arrival Of The First Reflection -- 17.2.4. Effect Of Loading Frequency On The Time Histories -- 17.2.5. Wavenumber COV For Different Material Property Distribution -- 17.2.6. Wavenumber Distributions For Different Type Of Input Distribution -- 17.2.7. Effect Of Material Uncertainty On Wavenumbers Obtained Using Higher-Order Theories -- 18.1. Theory Of Hyperelasticity -- 18.2. Non-Linear Governing Equation For An Isotropic Rod -- 18.3. Time Domain Finite Element Models For Hyperelastic Analysis -- 18.3.1. Standard Galerkin Finite Element Model (SGFEM) -- 18.3.2. Time Domain Spectral Finite Element Model (TDSFEM) -- 18.3.3. Taylor-Galerkin Finite Element Model (TGFEM) -- 18.3.4. Generalized Galerkin Finite Element Model (GGFEM) -- 18.4. Fsfem For Hyperelastic Wave Propagation -- 18.5. Numerical Results And Discussion -- 18.5.1. Performance Comparison Of Finite Element Schemes -- 18.5.2. Performance Of Frequency Domain Spectral Finite Element Model -- 18.5.3. Effect Of Non-Linearity On Wave Propagation In Hyperelastic Waveguides -- 18.5.4. Summary Of Numerical Efficiency Of Different Finite Element Schemes -- 18.6. Non-Linear Flexural Wave Propagation In Hyperelastic Timoshenko Beams -- 18.6.1. Numerical Results And Discussion.

Machine generated contents note: 1.1. Essential Components Of A Wave -- 1.1.1. Standing Waves -- 1.2. Need For Wave Propagation Analysis In Structures And Materials -- 1.3. Organization And Scope Of The Book -- 2.1. Introduction To The Theory Of Elasticity -- 2.1.1. Description Of Motion -- 2.1.2. Strain -- 2.1.3. Strain-Displacement Relations -- 2.1.4. Stress -- 2.1.5. Principal Stresses -- 2.1.6. Constitutive Relations -- 2.1.7. Elastic Symmetry -- 2.1.8. Governing Equations Of Motion -- 2.1.9. Dimensional Reduction Of 3D Elasticity Problems -- 2.1.10. Plane Problems In Elasticity: Reduction To Two Dimensions -- 2.1.11. Solution Procedures In Linear Theory Of Elasticity -- 2.2. Theory Of Gradient Elasticity -- 2.2.1. Eringen's Stress Gradient Theory -- 2.2.2. Strain Gradient Theory -- 3.1. Introduction To Composite Materials -- 3.2. Theory Of Laminated Composites -- 3.2.1. Micro-Mechanical Analysis Of Composites -- 3.2.2. Macro-Mechanical Analysis Of Composites -- 3.2.3. Classical Lamination Plate Theory -- 3.3. Introduction To Functionally Graded Materials (FGM) -- 3.3.1. Modeling Of FGM Structures -- 4.1. Fourier Transforms -- 4.1.1. Fourier Series -- 4.1.2. Discrete Fourier Transform -- 4.2. Short-Term Fourier Transform (STFT) -- 4.3. Wavelet Transforms -- 4.3.1. Daubechies Compactly Supported Wavelets -- 4.3.2. Discrete Wavelet Transform (DWT) -- 4.4. Laplace Transforms -- 4.4.1. Need For Numerical Laplace Transform -- 4.4.2. Numerical Laplace Transform -- 4.5. Comparative Merits And Demerits Of Different Transforms -- 5.1. Concept Of Wavenumber, Group Speeds, And Phase Speeds -- 5.2. Wave Propagation Terminologies -- 5.3. Spectral Analysis Of Motion -- 5.3.1. Second-Order System -- 5.3.2. Fourth-Order System -- 5.4. General Form Of Wave Equations And Their Characteristics -- 5.4.1. General Form Of Wave Equations -- 5.5. Different Methods Of Computing Wavenumbers And Wave Amplitudes -- 5.5.1. Method 1: The Companion Matrix And The SVD Technique -- 5.5.2. Method 2: Linearization Of PEP -- 6.1. Hamilton's Principle -- 6.2. Wave Propagation In 1D Elementary Waveguides -- 6.2.1. Longitudinal Wave Propagation In Rods -- 6.2.2. Flexural Wave Propagation In Beams -- 6.2.3. Wave Propagation In A Framed Structure -- 6.3. Wave Propagation In Higher-Order Waveguides -- 6.3.1. Wave Propagation In A Timoshenko Beam -- 6.3.2. Wave Propagation In A Mindlin-Herrmann Rod -- 6.4. Wave Propagation In Rotating Beams -- 6.5. Wave Propagation In Tapered Waveguides -- 6.5.1. Wave Propagation In A Tapered Rod With Exponential Depth Variation -- 6.5.2. Wave Propagation In A Tapered Rod With Polynomial Depth Variation -- 6.5.3. Wave Propagation In A Tapered Beam -- 7.1. Governing Equations Of Motion -- 7.1.1. Solution Of Navier's Equation -- 7.1.2. Propagation Of Waves In Infinite 2D Media -- 7.1.3. Wave Propagation In Semi-Infinite 2D Media -- 7.1.4. Wave Propagation In Doubly Bounded Media -- 7.1.5. Traction-Free Surfaces: A Case Of Lamb Wave Propagation -- 7.2. Wave Propagation In Thin Plates -- 7.2.1. Spectral Analysis -- 8.1. Wave Propagation In A 1D Laminated Composite Waveguide -- 8.1.1. Computation Of Wavenumbers -- 8.1.2. Wavenumber And Wave Speeds In 1D Elementary Composite Beams -- 8.2. Wave Propagation In Thick 1D Laminated Composite Waveguides -- 8.2.1. Wave Motion In Thick Composite Beam -- 8.3. Wave Propagation In Composite Cylindrical Tubes -- 8.3.1. Linear Wave Motion In Composite Tubes -- 8.3.2. Wave Propagation In Thin Composite Tubes -- 8.4. Wave Propagation In Two-Dimensional Composite Waveguides -- 8.4.1. Formulation Of Governing Equations And Computation Of Wavenumbers -- 8.5. Wave Propagation In 2D Laminated Composite Plates -- 8.5.1. Governing Equations And Wavenumber Computations -- 9.1. Wave Propagation In Sandwich Beams Based On Extended Higher-Order Sandwich Plate Theory (EHSAPT) -- 9.1.1. Governing Differential Equations -- 9.1.2. Wave Propagation Characteristics -- 9.2. Wave Propagation In 2D Sandwich Plate Wave-Guides -- 9.2.1. Governing Differential Equations -- 9.2.2. Computation Of Wave Parameters -- 9.2.3. Numerical Examples -- 10.1. Wave Propagation In Lengthwise Graded Rods -- 10.2. Wave Propagation In A Depthwise Graded FGM Beam -- 10.3. Wave Propagation On Lengthwise Graded Beam -- 10.4. Wave Propagation In 2D Functionally Graded Structures -- 10.5. Thermo-Elastic Wave Propagation In Functionally Graded Waveguides -- 11.1. Introduction To Nanostructures -- 11.1.1. Structure Of Carbon Nanotubes -- 11.2. Wave Propagation In MWCNTS Using The Local Euler-Bernoulli Model -- 11.2.1. Wave Parameters Computation -- 11.3. Wave Propagation In MWCNT Through A Local Shell Model -- 11.3.1. Governing Differential Equations -- 11.3.2. Calculation Of Wavenumbers -- 11.4. Wave Propagation In Non-Local Stress Gradient Nanorods -- 11.4.1. Governing Equations Of ESGT Nanorods -- 11.5. Axial Wave Propagation In Non-Local Strain Gradient Nanorods -- 11.5.1. Governing Equation For Second-Order Strain Gradient Model -- 11.5.2. Governing Equation For Fourth-Order Strain Gradient Model -- 11.5.3. Uniqueness And Stability Of SOSGT Nanorods -- 11.5.4. Axial Wave Propagation In SOSGT Nanorods -- 11.5.5. Axial Wave Characteristics Of The Fourth-Order SGT Model -- 11.5.6. Wave Propagation Analysis -- 11.6. Wave Propagation In Higher-Order Nanorods Using The ESGT Model -- 11.7. Wave Propagation In Nanobeams Using ESGT Formulations -- 11.7.1. Transverse Wave Propagation In The ESGT Model-Based Euler-Bernoulli Nanobeam -- 11.7.2. Transverse Wave Propagation In An ESGT Model-Based Timoshenko Nanobeam -- 11.8. Wave Propagation In Mwcnt Using The ESGT Model -- 11.8.1. Wave Dispersion In SWCNTS -- 11.8.2. Wave Dispersion In DWCNTS -- 11.9. Wave Propagation In Graphene -- 11.9.1. Governing Equations For Flexural Wave Propagation In Monolayer Graphene Sheets -- 11.9.2. Wave Dispersion Analysis -- 11.10. wave Propagation In Graphene In An Elastic Medium -- 11.10.1. Wave Dispersion Analysis -- 11.11. Wave Propagation In A Cnt-Reinforced Nanocomposite Beam -- 11.11.1. Governing Equation -- 11.11.2. Computation Of Wavenumbers And Group Speeds -- 12.1. Introductory Concepts -- 12.2. Variational Principles -- 12.2.1. Work And Complementary Work -- 12.2.2. Strain Energy And Complementary Strain Energy -- 12.2.3. Weighted Residual Techniques -- 12.2.4. Energy Functional -- 12.2.5. Weak Form Of The Governing Differential Equation -- 12.3. Energy Theorems -- 12.3.1. Principle Of Virtual Work -- 12.3.2. Principle Of Minimum Potential Energy (PMPE) -- 12.3.3. Rayleigh-Ritz Method -- 12.4. Finite Element Formulation: H -- Type Formulation -- 12.4.1. Shape Functions -- 12.4.2. Derivation Of Finite Element Equations -- 12.4.3. Isoparametric Formulation -- 12.4.4. Numerical Integration And Gauss Quadrature -- 12.4.5. Mass And Damping Matrix Formulation -- 12.5. Superconvergent Fe Formulation -- 12.5.1. Formulation Of A Superconvergent Laminated Composite FSDT Beam Element -- 12.6. Time Domain Spectral Finite Element Formulation- Ap -- Type Finite Element Formulation -- 12.6.1. Orthogonal Polynomials -- 12.7. Solution Methods For Finite Element Method -- 12.7.1. Finite Element Equation Solution In Static Analysis -- 12.7.2. Finite Element Equation Solution In Dynamic Analysis -- 12.8. Direct Time Integration -- 12.8.1. Explicit Time Integration Techniques -- 12.8.2. Implicit Time Integration -- 12.8.3. Newmark beta Method -- 12.9. Numerical Examples -- 12.9.1. Super-Convergent Beam Element -- 12.9.2. Time Domain Spectral FEM -- 12.10. modeling Guidelines For Wave Propagation Problems -- 13.1. Introduction To Spectral Finite Element Method -- 13.1.1. General Formulation Procedure Of SFEM: Fourier Transform -- 13.1.2. General Formulation Procedure: Wavelet Transform -- 13.1.3. General Formulation Procedure: Laplace Transform -- 13.2. Fourier Transform-Based Spectral Finite Element Formulation -- 13.2.1. Spectral Rod Element -- 13.2.2. Spectrally Formulated Elementary Beam Element -- 13.2.3. Higher-Order 1D Composite Waveguides -- 13.2.4. Spectral Element For Framed Structures -- 13.2.5. Wave Propagation Through An Angled Joint

-- 13.2.6. Composite 2D Layer Element -- 13.2.7. Propagation Of Surface And Interfacial Waves In Laminated Composites -- 13.2.8. Determination Of Lamb Wave Modes In Laminated Composites -- 13.2.9. Spectral Element Formulation For An Anisotropic Plate -- 13.2.10. Spectral Finite Element Formulation Of A Stiffened Composite Structure -- 13.2.11. Numerical Examples Wave Propagation In Stiffened Structures -- 13.2.12. Merits And Demerits Of Fourier Spectral Finite Element Method -- 13.2.13. Signal Wraparound Problems In FSFEM -- 13.3. Wavelet Transform-Based Spectral Finite Element Formulation -- 13.3.1. Governing Equations And Their Reduction To Ordinary Differential Equations -- 13.3.2. Periodic Boundary Conditions -- 13.3.3. Estimation Of Wavenumber And Group Speeds: Existence Of Artificial Dispersion -- 13.3.4. Non-Periodic Boundary Condition -- 13.3.5. Spectral Element Formulation -- 13.3.6. Numerical Examples -- 13.4. Laplace Transform-Based Spectral Finite Element Formulation -- 13.4.1. Analogy For The Numerical Damping Factor -- 13.4.2. Computation Of Wavenumbers And Group Speeds -- 13.4.3. Numerical Examples -- 14.1. Introduction -- 14.2. Constitutive Models For Piezoelectric Smart Composite Structures -- 14.2.1. Model For Piezoelectric Material

1