TY  - BOOK
AU  - Gopalakrishnan,S.
TI  - Wave propagation in materials and structures
SN  - 9781482262797
AV  - QC174.26.W28 G67 2017
U1  - 531/.1133 23
PY  - 2017///]
CY  - Boca Raton
PB  - CRC Press
KW  - Wave-motion, Theory of
KW  - Solids
KW  - Mathematics
KW  - Lightweight materials
KW  - fast
N1  - 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
ER  -