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1997 | Book | 2. edition

Introduction Read chapter Read first chapter

Wave Propagation in Structures

Spectral Analysis Using Fast Discrete Fourier Transforms

Author: James F. Doyle

Publisher: Springer New York

Book Series : Mechanical Engineering Series

Included in: Professional Book Archive

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About this book

Mechanical engineering. an engineering discipline borne of the needs of the in­ dustrial revolution. is once again asked to do its substantial share in the call for industrial renewal. The general call is urgent as we face profound issues of produc­ tivity and competitiveness that require engineering solutions. among others. The Mechanical Engineering Series features graduate texts and research monographs intended to address the need for information in contemporary areas of mechanical engineering. The series is conceived as a comprehensive one that covers a broad range of concentrations important to mechanical engineering graduate education and re­ search. We are fortunate to have a distinguished roster of consulting editors on the advisory board. each an expert in one the areas of concentration. The names of the consulting editors are listed on the facing page of this volume. The areas of concentration are: applied mechanics; biomechanics; computational mechan­ ics; dynamic systems and control; energetics; mechanics of materials; processing; thermal science; and tribology.

Table of Contents

Frontmatter
Introduction
Abstract
This small book is an introduction to the spectral analysis method as a means of solving wave propagation problems in structures. The emphasis is on practical methods from both the computational and applications aspects, and reference to experimental results is made whenever possible.
James F. Doyle
1. Spectral Analysis of Wave Motion
Abstract
It has long been known that an arbitrary time signal can be thought of as the superposition of many sinusoidal components, that is, it has a distribution or spectrum of components. Working in terms of the spectrum is called spectral analysis. In wave analysis, the time domain for a motion or response is from minus infinity to plus infinity. Functions in this domain are represented by a continuous distribution of components which is known as its continuous Fourier transform (CFT). However, the numerical evaluation and manipulation of the components requires discretizing the distribution in some manner — the one chosen here is by way of the discrete Fourier transform (DFT). This has the significant advantage that it allows the use of the very efficient fast Fourier transform (FFT) computer algorithm.
James F. Doyle
2. Longitudinal Waves in Rods
Abstract
Rods and struts are very important structural elements and form the basis of many truss and grid frameworks. Since their load bearing capability is axial, then as waveguides they conduct only longitudinal wave motion.
James F. Doyle
3. Flexural Waves in Beams
Abstract
A beam is a long slender member designed to support lateral loads. In doing so, the displacement is predominantly transverse to the centerline, and internal shear forces and bending moments are generated. The dynamic behavior of beams is called flexural motion.
James F. Doyle
4. Higher-Order Waveguides
Abstract
The waveguide theories of the last two chapters were based on some elementary mechanics modeling; the question obviously arises as to the adequacy of these models. We will try to clarify the issues involved by considering some exact solutions of waves in waveguides; this is a difficult and mathematically cumbersome area so only a limited number of aspects will be treated. The chapter begins by looking at waves in extended media and waves in bounded media as illustrated in Figure 4.1. Perhaps the most important insight into the functioning of the exact waveguides is the number of modes they support — in fact, they support an infinity of modes. We will show that the behavior of these modes was anticipated by considering the effects of elastic constraint in the elementary models.
James F. Doyle
5. The Spectral Element Method
Abstract
The only way to efficiently handle wave propagation problems in structures with complicated boundaries and discontinuities is to develop a matrix methodology for use on a computer. In this chapter, we develop such a method.
James F. Doyle
6. Waves in Thin Plates
Abstract
A plate is a body where one of the dimensions is substantially smaller than the other two. Plates in flexure are the two-dimensional equivalent of beams and classical plate theory is its equivalent of the Bernoulli-Euler beam theory, whereas the in-plane or membrane behavior of plates is analogous to that of rods. Many of the behaviors of plates and beams are quite similar, therefore only those aspects that are significantly different will be covered in this chapter.
James F. Doyle
7. Structure-Fluid Interaction
Abstract
There are many practical situations where the interaction between the dynamics of a structure and a surrounding fluid is of great importance. The most obvious is noise; noise is the propagation of acoustic energy through the fluid. The interaction can also influence the response of the structure itself; examples include dams, chimney stacks, ships, fuselages, propellers, and transmission cables.
James F. Doyle
8. Thin-Walled Structures
Abstract
The thin-walled structures of interest in this chapter are generally enclosed regions, as typified by an aircraft fuselage. They are modeled as combinations of folded plates and cylindrical shell segments as shown in Figure 8.1. Other examples of structures which fall into this category include plates with stringers, corrugations, channels, ducts, troughs, open and closed thin-walled tubes with one or more cells.
James F. Doyle
Backmatter
Metadata
Title
Wave Propagation in Structures
Author
James F. Doyle
Copyright Year
1997
Publisher
Springer New York
Electronic ISBN
978-1-4612-1832-6
Print ISBN
978-1-4612-7304-2
DOI
https://doi.org/10.1007/978-1-4612-1832-6