Spectral Finite Element Method: Wave Propagation, Diagnostics and Control in Anisotropic and Inhomogeneous Structures

S. Gopalakrishnan PhD, A. Chakraborty PhD, D. Roy Mahapatra PhD (auth.)1846283558, 9781846283550

In recent times, the use of composites and functionally graded materials (FGMs) in structural applications has increased. FGMs allow the user to design materials for a specified functionality and therefore have numerous uses in structural engineering. However, the behavior of these structures under high-impact loading is not well understood. Spectral Finite Element Method: Wave Propagation, Diagnostics and Control in Anisotropic and Inhomogeneous Structures focuses on some of the wave propagation and transient dynamics problems with these complex media which had previously been thought unmanageable.

By using state-of-the-art computational power, the Spectral Finite Element Method (SFEM) can solve many practical engineering problems. This book is the first to apply SFEM to inhomogeneous and anisotropic structures in a unified and systematic manner. The authors discuss the different types of SFEM for regular and damaged 1-D and 2-D waveguides, various solution techniques, different methods of detecting the presence of damages and their locations, and different methods available to actively control the wave propagation responses. The theory is supported by tables, figures and graphs; all the numerical examples are designed to bring out the essential wave behavior in these complex structures. Some case studies based on real-world problems are also presented.

This book is intended for senior undergraduate students and graduate students studying wave propagation in structures, smart structures, spectral finite element method and structural health monitoring. Readers will gain a complete understanding of how to formulate a spectral finite element; learn about wave behavior in inhomogeneous and anisotropic media; and, discover how to design some diagnostic tools for monitoring the health or integrity of a structure. The book will also be of value to researchers and practicing engineers in structural integrity.

Table of contents :
Front Matter….Pages i-xiv
Introduction….Pages 1-22
Introduction to the Theory of Anisotropic and Inhomogeneous Materials….Pages 23-39
Idealization of Wave Propagation and Solution Techniques….Pages 41-54
Wave Propagation in One-dimensional Anisotropic Structures….Pages 55-122
Wave Propagation in One-dimensional Inhomogeneous Structures….Pages 123-169
Wave Propagation in Two-dimensional Anisotropic Structures….Pages 171-193
Wave Propagation in Two-dimensional Inhomogeneous Structures….Pages 195-248
Solution of Inverse Problems: Source and System Identification….Pages 249-257
Application of SFEM to SHM: Simplified Damage Models….Pages 259-306
Application of SFEM to SHM: Efficient Damage Detection Techniques….Pages 307-363
Spectral Finite Element Method for Active Wave Control….Pages 365-422
Back Matter….Pages 423-440