Elastic Wave Propagation in Structures and Materials

✍ Scribed by Srinivasan Gopalakrishnan

• Publisher: CRC Press
• Year: 2022
• Tongue: English
• Leaves: 430
• Edition: 1
• Category: Library

✦ Synopsis

Elastic Wave Propagation in Structures and Materials initiates with a brief introduction to wave propagation, different wave equations, integral transforms including fundamentals of Fourier Transform, Wavelet Transform, Laplace Transform and their numerical implementation. Concept of spectral analysis and procedure to compute the wave parameters, wave propagation in 1-D isotropic waveguides, wave dispersion in 2-D waveguides is explained. Wave propagation in different media such as laminated composites, functionally graded structures, granular soils including non-local elasticity models is addressed. The entire book is written in modular form and analysis is performed in frequency domain.

Features:

• Brings out idea of wave dispersion and its utility in the dynamic responses.

• Introduces concepts as Negative Group Speeds, Einstein’s Causality and escape frequencies using solid mathematical framework.

• Discusses the propagation of waves in materials such as laminated composites and functionally graded materials.

• Proposes spectral finite element as analysis tool for wave propagation.

• Each concept/chapter supported by homework problems and MATLAB/FORTRAN codes.

This book aims at Senior Undergraduates and Advanced Graduates in all streams of engineering especially Mechanical and Aerospace Engineering.

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Contents
Preface
Author Biography
CHAPTER 1: Introduction to Wave Propagation
1.1. ESSENTIAL COMPONENTS OF A WAVE
1.2. INTERFERENCE OF WAVES
1.2.1. Interference of Two Similar Waves Propagating in the Same Direction
1.2.2. Standing Waves
1.3. NEED FOR WAVE PROPAGATION ANALYSIS IN STRUCTURES AND MATERIALS
1.4. SOME WAVE PROPAGATION PROBLEMS IN SCIENCE AND ENGINEERING
1.5. ORGANIZATION AND SCOPE OF THE BOOK
CHAPTER 2: Introduction to Fourier Transforms
2.1. FOURIER TRANSFORMS
2.1.1. Continuous Fourier Transforms (CFT)
2.1.2. Fourier Series
2.1.3. Discrete Fourier Transform
2.2. COMPARATIVE MERITS AND DEMERITS OF FFT
NOTE ON MATLAB® SCRIPTS PROVIDED IN THIS CHAPTER
SUMMARY
EXERCISES
CHAPTER 3: Introduction to Wave Propagation in Structures
3.1. CONCEPT OF WAVENUMBER, GROUP SPEEDS AND PHASE SPEEDS
3.2. WAVE PROPAGATION TERMINOLOGIES
3.3. SPECTRAL ANALYSIS OF MOTION
3.3.1. Second-Order System
3.3.2. Fourth-Order System
3.4. GENERAL FORM OF WAVE EQUATION AND THEIR CHARACTERISTICS
3.4.1. General Form of Wave Equations
3.4.2. Characteristics of Waves in Anisotropic Media
3.4.3. Characteristics of Waves in Inhomogeneous Media
3.4.4. Characteristics of Waves in Non-local Waveguides
3.5. DIFFERENT METHODS OF COMPUTING WAVENUMBERS AND WAVE AMPLITUDES
3.5.1. Method - 1 : The Companion Matrix & the SVD Technique
3.5.2. Method - 2 : Linearization of Polynomial Eigenvalue Problem (PEP)
SUMMARY
EXERCISES
CHAPTER 4: Wave Propagation in One-Dimensional Isotropic Structural Waveguides
4.1. WAVE PROPAGATION IN 1-D ELEMENTARY WAVEGUIDES
4.2. LONGITUDINAL WAVE PROPAGATION IN RODS
4.2.1. D’Alemberts Solution
4.2.2. Spectral Analysis
4.2.3. Propagation of Waves in an Infinite Longitudinal Waveguide
4.2.4. Interaction of Waves with Fixed and Free Boundaries
4.2.5. Reflection from an Elastic Boundary
4.2.6. Reection and Transmission from a Joint Having Concentrated Mass and Stepped Rod
4.3. FLEXURAL WAVE PROPAGATION IN BEAMS
4.3.1. Wave Propagation Analysis
4.3.2. Propagation of Waves in an Infinite Beam
4.3.3. Reflection from Boundaries
4.3.4. Reflection from Elastic Boundary
4.3.5. Reection and Transmission from a Stepped Beam and a Joint with Concentrated Mass
4.3.6. Wave Propagation in Beams with Pre-Tension or Pre-Compression
4.3.7. Wave Propagation in a Beam on Elastic Foundation
4.3.8. Wave Propagation in a Framed Structure
4.4. WAVE PROPAGATION IN HIGHER-ORDER WAVEGUIDES
4.4.1. Wave Propagation in Timoshenko Beam
4.4.2. Wave Propagation in Mindlin-Herrmann Rod
4.5. WAVE PROPAGATION IN ROTATING BEAMS
4.6. WAVE PROPAGATION IN TAPERED WAVEGUIDES
4.6.1. Wave Propagation in Tapered Rod Having Exponential Depth Variation
4.6.2. Wave Propagation in Tapered Rod Having Polynomial Depth Variation
4.6.3. Wave Propagation in Tapered Beam
NOTE ON MATLAB® SCRIPTS PROVIDED IN THIS CHAPTER
SUMMARY
EXERCISES
CHAPTER 5: Wave Propagation in Viscoelastic Waveguides
5.1. CONSTITUTIVE MODELS FOR VISCOELASTIC WAVEGUIDES
5.1.1. Two-Parameter Models
5.1.2. Three-Parameter Models
5.2. WAVE PROPAGATION IN VISCOELASTIC ROD
5.2.1. Wave Propagation in Two-Parameter Viscoelastic Rod
5.2.2. Wave Propagation in Three-Parameter Viscoelastic Rod
5.3. WAVE PROPAGATION IN VISCOELASTIC BEAMS
NOTE ON MATLAB® SCRIPTS PROVIDED IN THIS CHAPTER
SUMMARY
EXERCISES
CHAPTER 6: Signal Processing Aspects in Wave Propagation
6.1. SIGNAL PROCESSING ISSUES OF SAMPLED WAVEFORMS
6.1.1. Signal Aliasing
6.1.2. Spectral Leakage and Windowing
6.1.3. Signal Wraparound Problem
6.2. PROPAGATION AND RECONSTRUCTION OF SIGNALS
6.2.1. Integration of the Signals
SUMMARY
EXERCISES
CHAPTER 7: Wave Propagation in Two-Dimensional Isotropic Waveguides
7.1. GOVERNING EQUATIONS OF MOTION
7.2. SOLUTION OF NAVIER’S EQUATION
7.3. PROPAGATION OF WAVES IN INFINITE 2-D MEDIA
7.3.1. Propagation of P-waves
7.3.2. Propagation of SV Waves
7.3.3. Propagation of SH Waves
7.4. WAVE PROPAGATION IN SEMI-INFINITE 2-D MEDIA
7.4.1. Fixed Boundary Condition
7.4.2. Mixed Boundary Condition
7.4.3. Traction Free Boundary Conditions: A Case of Rayleigh Surface Waves
7.5. WAVE PROPAGATION IN DOUBLY BOUNDED MEDIA
7.5.1. Symmetric Loading Case
7.5.2. Fixed Boundary Condition
7.5.3. Method of Solution of Dispersion Equations in a Doubly Bounded Media
7.5.4. Mixed Boundary Condition: Case I
7.5.5. Mixed Boundary Condition: Case II
7.5.6. Traction Free Surfaces: A Case of Lamb Wave Propagation
7.6. WAVE PROPAGATION IN THIN PLATES
7.6.1. Spectral Analysis
7.6.2. Plate Edge Wave Propagation
Wavenumber Transform Solution
NOTE ON MATLAB® SCRIPTS PROVIDED IN THIS CHAPTER
SUMMARY
EXERCISES
CHAPTER 8: Wave Propagation in Laminated Composite Waveguides
8.1. INTRODUCTION TO COMPOSITE MATERIALS
8.2. THEORY OF LAMINATED COMPOSITES
8.2.1. Micro-mechanical Analysis of Composites
8.2.2. Macro-mechanical Analysis of Composites
8.3. CLASSICAL LAMINATION PLATE THEORY
8.4. WAVE PROPAGATION IN 1-D THIN LAMINATED COMPOSITE WAVEGUIDE
8.4.1. Computation of Wavenumbers
8.5. WAVE PROPAGATION IN THICK 1-D LAMINATED COMPOSITE WAVEGUIDES
8.5.1. Governing Equation for a Thick Composite Beam
8.5.2. Wave Propagation in a Thick Beam Model with Both Shear Deformation and Lateral Contraction Included
8.5.3. Wave Propagation in a Thick Beams Model That Includes Only the Shear Deformation
8.6. WAVE PROPAGATION IN TWO-DIMENSIONAL COMPOSITE WAVEGUIDES
8.6.1. Formulation of Governing Equations and Computation of Wavenumbers
8.7. WAVE PROPAGATION IN 2-D LAMINATED COMPOSITE PLATES
8.7.1. Governing Equations and Wavenumber Computations
NOTE ON MATLAB® SCRIPTS PROVIDED IN THIS CHAPTER
SUMMARY
EXERCISES
CHAPTER 9: Wave Propagation in Graded Material Waveguides
9.1. INTRODUCTION TO FUNCTIONALLY GRADED MATERIALS (FGM)
9.2. MODELING OF FGM STRUCTURES
9.3. WAVE PROPAGATION IN LENGTHWISE GRADED RODS
9.4. WAVE PROPAGATION IN DEPTHWISE GRADED FGM BEAM
9.4.1. Reduction to FSDT
9.5. WAVE PROPAGATION ON LENGTHWISE GRADED BEAM
9.6. WAVE PROPAGATION IN 2-D FUNCTIONALLY GRADED STRUCTURES
NOTE ON MATLAB® SCRIPTS PROVIDED IN THIS CHAPTER
SUMMARY
EXERCISES
CHAPTER 10: Wave Propagation in Granular Medium
10.1. MECHANICAL PROPERTIES EVALUATION FOR DRY SANDS
10.2. WAVE PROPAGATION CHARACTERISTICS IN DIFFERENT TYPES OF DRY SANDS
10.3. DESIGN CONCEPT FOR SAND BUNKERS FOR EFFICIENT BLAST MITIGATION
10.4. RESPONSE OF SAND BUNKERS SUBJECTED TO BLAST LOADING
10.4.1. Estimation of Blast Pressure Profile on the Sand Bunker
SUMMARY
EXERCISES
CHAPTER 11: Wave Propagation in Non-Local One-Dimensional Waveguides
11.1. ERINGEN’S STRESS GRADIENT THEORY
11.2. STRAIN GRADIENT THEORY
11.3. WAVE PROPAGATION IN NO-NLOCAL WAVEGUIDES
11.3.1. Wave Propagation in Eringen Stress Gradient Rod (ESGR)
11.3.2. Wave Propagation in Second-Order Strain Gradient Rod (SOSGR-P) Model
11.3.3. Wave Propagation in Second-Order Strain Gradient Rod (SOSGR-N) Model
11.3.4. Wave Propagation in Fourth-Order Strain Gradient Rod (FOSGR) Model
11.3.5. Wave Propagation in Euler-Bernoulli Eringen Stress Gradient Beam (ESGB)
NOTE ON MATLAB® SCRIPTS PROVIDED IN THIS CHAPTER
SUMMARY
EXERCISES
CHAPTER 12: Introduction to Spectral Finite Element Formulation
12.1. FUNDAMENTAL PRINCIPLES OF SPECTRAL FINITE ELEMENT FORMULATION
12.2. GENERAL FORMULATION PROCEDURE OF SFEM
12.3. SPECTRAL FINITE ELEMENT FORMULATION
12.3.1. Spectral Rod Element
12.3.2. Spectrally Formulated Elementary Beam Element
12.3.3. Higher-Order 1-D Composite Waveguides
12.3.4. Spectral Element for Framed Structures
12.3.5. 2-D Layer Element for Isotropic Solids
One Noded or Throw-off Element
Two Noded or Finite Length Element
12.3.6. Composite Layer Element
Finite Layer Element (FLE)
Infinite Layer Element (ILE)
12.3.7. Determination of Lamb Wave Modes in Laminated Composites
12.4. MERITS AND DEMERITS OF FOURIER SPECTRAL FINITE ELEMENT METHOD
SUMMARY
EXERCISES
Bibliography
Index