Wave Propagation in Structures (Mechanical Engineering Series)

✍ Scribed by James F. Doyle

• Publisher: Springer
• Year: 2020
• Tongue: English
• Leaves: 432
• Edition: 3rd ed. 2021
• Category: Library

✦ Synopsis

This third edition builds on the introduction of spectral analysis as a means of investigating wave propagation and transient oscillations in structures. Each chapter of the textbook has been revised, updated and augmented with new material, such as a modified treatment of the curved plate and cylinder problem that yields a relatively simple but accurate spectral analysis. Finite element methods are now integrated into the spectral analyses to gain further insights into the high-frequency problems. In addition, a completely new chapter has been added that deals with waves in periodic and discretized structures. Examples for phononic materials meta-materials as well as genuine atomic systems are given.

✦ Table of Contents

Preface
Contents
Notation
Reference
Introduction
What Is Spectral Analysis?
Structures and Waveguides
Wave Propagation and Vibrations
Themes and Threads
A Question of Units
References
1 Spectral Analysis of Wave Motion
1.1 Fourier Transforms
1.1.1 Continuous Fourier Transforms
1.1.2 Discrete Fourier Transform
1.1.3 Fast Fourier Transform Algorithm
1.1.4 Space Distributions Using Fourier Series
1.2 Applications Using the FFT Algorithm
1.2.1 Explorations of the Properties
1.2.2 Experimental Aspects of Wave Signals
1.3 Spectral Analysis of Wave Motion
1.3.1 General Functions of Space-Time and Spectrum Relations
1.3.2 Some Wave Examples
1.3.3 Group Speed
1.3.4 Summary of Wave Relations
1.4 Propagating and Reconstructing Waves
1.4.1 Basic Algorithm
1.4.2 Integration of Signals
Further Research
Further Research
References
2 Longitudinal Waves in Rods
2.1 Elementary Rod Modeling
2.1.1 Equation of Motion and Spectral Analysis
2.1.2 Basic Solution for Waves in Rods
2.2 Dissipation in Rods
2.2.1 Distributed Constraint
2.2.2 Viscoelastic Rod
2.3 Coupled Thermoelastic Waves
2.3.1 Governing Equations
2.3.2 The Spectrum Relation
2.3.3 Blast Loading of a Rod
2.4 Reflection and Transmission of Waves
2.4.1 Reflection from an Elastic Boundary
2.4.2 Reflection from an Oscillator
2.4.3 Concentrated Mass Connecting Two Rods
2.4.4 Interactions at a Distributed Elastic Joint
2.5 Distributed Loading
2.5.1 Periodically Extended Load Model
2.5.2 Connected Waveguide Solution
Further Research
Further Research
References
3 Flexural Waves in Beams
3.1 Bernoulli–Euler Beam Modeling
3.1.1 Equations of Motion and Spectral Analysis
3.1.2 Basic Solution for Waves in Beams
3.1.3 Beam with Axial Load
3.2 Bernoulli–Euler Beam with Constraints
3.2.1 Beam on an Elastic Foundation
3.2.2 Coupled Beam Structure
3.3 Reflection and Transmission of Flexural Waves
3.3.1 Reflections from Simple Ends
3.3.2 Reflections and Transmissions at a General Joint
3.4 Curved Beams
3.4.1 Deformation of Curved Beams
3.4.2 Spectrum Relation
3.4.3 Impact of a Curved Beam
Further Research
Further Research
References
4 Higher Order Waveguide Models
4.1 Waves in Infinite and Semi-Infinite Media
4.1.1 Navier's Equations and Helmholtz Potentials
4.1.2 Constructing Potentials Appropriate for Boundaries
4.1.3 Forced Response of a Semi-Infinite Plane
4.1.4 Free-Edge Waves: Rayleigh Surface Waves
4.2 Waves in Doubly Bounded Media
4.2.1 Forced Responses
4.2.2 Spectrum Relations for Free-Wave Responses
4.2.3 Discussion of Lamb Waves in Structural Waveguides
4.3 Variational Formulation of Dynamic Equilibrium
4.3.1 Work and Strain Energy in a General Body
4.3.2 Virtual Work and Hamilton's Principle
4.3.3 Illustrative Application of the Ritz Semi-direct Method
4.4 Refined Beam Models
4.4.1 Timoshenko Beam Model
4.4.2 Adjustable Parameters
4.4.3 Spectrum Relation
4.4.4 Impact of a Timoshenko Beam
4.5 Refined Rod Models
4.5.1 Love One-Mode Model
4.5.2 Mindlin–Herrmann Two-Mode Model
4.5.3 Three-Mode Model
4.6 N-Mode Rod Model
4.6.1 Kinematic Assumptions
4.6.2 Spectrum and Dispersion Relations
Further Research
Further Research
References
5 The Spectral Element Method
5.1 Structures as Connected Waveguides
5.2 Spectral Element for Rods
5.2.1 Shape Functions
5.2.2 Dynamic Stiffness for Rods
5.2.3 Simple Examples
5.2.4 Nodal Representation of Distributed Loadings
5.3 Spectral Element for Beams
5.3.1 Shape Functions
5.3.2 Dynamic Stiffness for Beams
5.4 General Frame Structures
5.4.1 Member Stiffness Matrix Referred to Global Axes
5.4.2 Structural Stiffness Matrix
5.4.3 Some Programming Considerations
5.4.4 An Application
5.4.5 Periodic Structures and the Transfer Matrix
5.4.6 Long Truss Structure
5.5 Spectral Super-Elements
5.5.1 Formulation of a Spectral Super-Element
5.5.2 Assemblage of Super-Element Stiffnesses
5.5.3 Example of an Angle Joint
5.5.4 Recovery of Internal Displacements and Forces
5.5.5 Periodic Structures
5.6 Impact Force Identification
5.6.1 Wave Propagation Responses
5.6.2 Frequency Domain Deconvolution
5.6.3 Examples of Force Identification
Further Research
Further Research
References
6 Waves in Plates and Cylinders
6.1 Models of Plates in Flexure
6.1.1 Mindlin Plate Model
6.1.2 Flexural Behavior of Very Thin Plates
6.1.3 Spectral Analysis of Thin Plates
6.1.4 Constructing Simpler Waveguide Models
6.2 Arbitrarily Crested Waves
6.2.1 Point Impact of a Plate
6.2.2 Point Impact Using Wavenumber Summations (pEL Method)
6.3 Reflection and Scattering of Flexural Waves
6.3.1 Waves Reflected from a Straight Edge
6.3.2 Free-Edge Waves
6.3.3 Scattering of Flexural Waves
6.4 Waves in Cylinders and Curved Plates
6.4.1 Deformation of Cylindrical Shells
6.4.2 Wave Propagation Along a Cylinder
6.4.3 Curved Plate Equations
6.4.4 Spectrum Relation for Propagation in the Hoop Direction
6.4.5 Donnell Shell Equations
Further Research
Further Research
References
7 Thin-Walled Structures
7.1 Spectral Elements for Flat Plates
7.1.1 Membrane Spectral Elements
7.1.2 Flexure Spectral Elements
7.1.3 A Simple Example
7.2 Folded Plate Structures
7.2.1 Structural Stiffness Matrix
7.2.2 Computer Program Structure
7.2.3 Structural Applications
7.3 Spectral Elements for Curved Plates
7.3.1 Impact of an Infinite Curved Plate
7.3.2 General Shape Functions
7.3.3 Dynamic Stiffness Relation for a Curved Shell Element
7.3.4 Point Loading of a Complete Cylinder
Further Research
Further Research
References
8 Structure–Fluid Interactions
8.1 Plate–Fluid Interactions
8.1.1 Linearized Acoustic Wave Equations
8.1.2 Incident Plane Wave on a Plate
8.2 Panel Excitations
8.2.1 Line Loading of an Infinite Plate in a Fluid
8.2.2 Double Panel Systems
8.2.3 Cylindrical Cavity
8.2.4 Comparison of Fluid Loadings
8.3 Waveguide Modeling of Distributed Pressures
8.3.1 Free Wave Response
8.3.2 Modified Spectrum Relations
8.4 Radiation from Finite Plates
8.4.1 Finite Plate Response
8.4.2 Fluid Response from a Finite Plate
8.4.3 Far-Field Approximation
Further Research
Further Research
References
9 Discrete and Discretized Structures
9.1 Wave Propagation in 1D Discrete Systems
9.1.1 Beaded String
9.1.2 Two-Mass String
9.1.3 Chains with Internal Structure
9.2 Wave Propagation in Anisotropic Systems
9.2.1 Elastic Anisotropic Solids
9.2.2 2D Anisotropic Systems
9.3 Atomic Lattice Structures
9.3.1 Lennard-Jones Potentials
9.3.2 Atomistic Models of Elasticity
9.3.3 Embedded Atom Models (EAM)
9.3.4 Continuum Models for Discrete Systems
9.4 Spectral Analyses of FE Discretized Systems
9.4.1 Spectrum Relations from Element Stiffness
9.4.2 Real-Only Spectrum Relations and Spectral Shapes
Further Research
Further Research
References
Afterword
AppendixA
A.1 Bessel Functions
A.1.1 Bessel Equations and Solutions
A.1.2 Limiting Behavior
References
Index