1st Edition
Elastic Wave Propagation in Structures and Materials
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.
Chapter 1 Introduction to Wave Propagation
1.1 ESSENTIAL COMPONENTS OF A WAVE
1.2 INTERFERENCE OF WAVES
1.3 NEED FOR WAVE PROPAGATION ANALYSIS IN STRUCTURES AND MATERIALS
1.4 SAMPLE 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
2.2 COMPARATIVE MERITS AND DEMERITS OF FFT
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
3.4 GENERAL FORM OF WAVE EQUATION AND THEIR CHARACTERISTICS
3.5 DIFFERENT METHODS OF COMPUTING WAVENUMBERS, AND WAVE AMPLITUDES
Chapter 4 Wave Propagation in One Dimensional Isotropic Structural Waveguides
4.1 WAVE PROPAGATION IN 1D ELEMENTARY WAVEGUIDES
4.2 LONGITUDINAL WAVE PROPAGATION IN RODS
4.3 FLEXURAL WAVE PROPAGATION IN BEAMS
4.4 WAVE PROPAGATION IN HIGHER ORDER WAVEGUIDES
4.5 WAVE PROPAGATION IN ROTATING BEAMS
4.6 WAVE PROPAGATION IN TAPERED WAVEGUIDES
Chapter 5 Wave Propagation in Viscoelastic Waveguides
5.1 CONSTITUTIVE MODELS FOR VISCOELASTIC WAVEGUIDES
5.2 WAVE PROPAGATION IN VISCOELASTIC ROD
5.3 WAVE PROPAGATION IN VISCOELASTIC BEAMS
Chapter 6 Signal Processing Aspects in Wave Propagation
6.1 SIGNAL PROCESSING ISSUES OF SAMPLED WAVEFORMS
6.2 PROPAGATION AND RECONSTRUCTION OF SIGNALS
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 2D MEDIA
7.4 WAVE PROPAGATION IN SEMIINFINITE 2D MEDIA
7.5 WAVE PROPAGATION IN DOUBLY BOUNDED MEDIA
7.6 WAVE PROPAGATION IN THIN PLATES
Chapter 8 □ Wave Propagation in Laminated Composite Waveguides
8.1 INTRODUCTION TO COMPOSITE MATERIALS
8.2 THEORY OF LAMINATED COMPOSITES
8.3 CLASSICAL LAMINATION PLATE THEORY
8.4 WAVE PROPAGATION IN 1D THIN LAMINATED COMPOSITE WAVEGUIDE
8.5 WAVE PROPAGATION IN THICK 1D LAMINATED COMPOSITE WAVEGUIDES
8.6 WAVE PROPAGATION IN TWO DIMENSIONAL COMPOSITE WAVEGUIDES
8.7 WAVE PROPAGATION IN 2D LAMINATED COMPOSITE PLATES
Chapter 9 Wave Propagation in Graded Material Waveguides
9.1 INTRODUCTION TO FUNCTIONALLY GRADED MATERIALS (FGM)
9.2 MODELLING OF FGM STRUCTURES
9.3 WAVE PROPAGATION IN LENGTHWISE GRADED RODS
9.4 WAVE PROPAGATION IN DEPTHWISE GRADED FGM BEAM
9.5 WAVE PROPAGATION ON LENGTHWISE GRADED BEAM
9.6 WAVE PROPAGATION IN 2D FUNCTIONALLY GRADED STRUCTURES
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
Chapter 11 Wave Propagation in NonLocal One Dimensional Waveguides
11.1 ERINGEN’S STRESS GRADIENT THEORY
11.2 STRAIN GRADIENT THEORY
11.3 WAVE PROPAGATION IN NONLOCAL WAVEGUIDES
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
12.4 MERITS AND DEMERITS OF FOURIER SPECTRAL FINITE ELEMENT METHOD
Biography
Prof. Gopalakrishnan received his Master’s Degree in Engineering Mechanics from Indian Institute of Technology, Madras, Chennai and Ph.D from School of Aeronautics and Astronautics from Purdue University, USA in the year December 1992. After his Ph.D., he was a Postdoctoral Fellow in the department of Mechanical Engineering at Georgia Institute of Technology. In the year November 1997, he joined the Department of Aerospace Engineering at Indian Institute of Science Bangalore, where currently he is a senior Professor. His main areas of interest are Wave Propagation in complex media, Computational Mechanics, Smart Structures, and Structural Health Monitoring. He has publisher 218 refereed international journal publications and has authored 9 textbooks and monographs and has an h-index of 50 in Google scholar. He is in the editorial board of 6 international journals and is the Associate editor for Smart Materials and Structures and Structural Health Monitoring international journals. Prof. Gopalakrishnan is decorated with many awards and honors, which include, International Structural Health Monitoring person of the year awards 2016 instituted by SAGE Publications, Fellow of Indian National Academy of Engineering, Fellow of Indian Academy of Sciences, Associate Fellows AIAA, Distinguished Alumnus Award, Indian Institute of Technology, Madras, Chennai, Satish Dhawan Young Scientist Award by Government of Karnataka, Biren Roy Trust award of Aeronautical society of India, Alumni Award of excellence in research at IISc and the Royal Academy of Engineering, UK Distinguished visiting Fellowship. Recently He was elected Fellow of Institute of Mechanical Engineers, UK in the year 2020.
