1 Spectral Analysis and the FFT.- 1.1 Continuous Fourier Transforms.- 1.2 Properties of Fourier Transforms.- 1.3 Fourier Series.- 1.4 Discrete Fourier Transform.- 1.5 Special Forms of the Discrete Transform.- 1.6 Fast Fourier Transform Algorithm.- 1.7 Examples Using the FFT Algorithm.- 1.8 Sampled Waveforms.- 2 Spectral Analysis of Wave Motion.- 2.1 Spectral Analysis of Differential Equations.- 2.2 Examples.- 2.3 Propagating and Reconstructing Waves.- 2.4 Wave Behavior of the Motion.- 2.5 Experimental Aspects of Wave Propagation.- 2.6 Signal Processing and Spectral Estimation.- 3 Longitudinal Waves in Rods.- 3.1 Elementary Rod Theory.- 3.2 Basic Solution for Waves in Rods.- 3.3 Reflection from Boundaries.- 3.4 Reflections and Transmissions.- 3.5 Coupled Thermoelastic Waves.- 3.6 Generalized Rod.- 3.7 Mindlin-Herrmann Rod Theory.- 4 Flexural Waves in Beams.- 4.1 Bernoulli-Euler Beam Theory.- 4.2 Basic Solution for Waves in Beams.- 4.3 Boundary Reflections of Flexural Waves.- 4.4 Reflections and Transmissions.- 4.5 Curved Beams.- 4.6 Remote Sensing.- 4.7 General Bernoulli-Euler Beam.- 4.8 Timoshenko Beam Theory.- 5 Wave Propagation in Structures.- 5.1 Truss and Frame Analysis.- 5.2 Structural Stiffness Matrix.- 5.3 Matrix Formulation of Inertia Effects.- 5.4 Spectral Element for Rods.- 5.5 Spectral Element for Beams.- 5.6 Structural Formulation.- 5.7 Structural Applications.- 6 Waves in Two Dimensions.- 6.1 Waves in Infinite Media.- 6.2 Semi-infinite Media.- 6.3 Doubly Bounded Media.- 6.4 Flexural Behavior of Plates.- 6.5 Reflections from Boundaries.- 6.6 Point Impact of a Plate.- 6.7 Double Series Solution for Arbitrary Waves.- 6.8 Anisotropic Plates.- Afterword.- A Contact Force.- B Bessel Functions.- C Examples Parameters.- D Source Code Listings.- References.
The study of wave propagation seems very remote to many engineers, even to those who are involved in structural dynamics. I think one of the reasons for this is that the examples usually taught in school were either so simple as to be inapplicable to real world problems, or so mathematically abstruse as to be intractable. This book contains an approach, spectral analysis, that I have found to be very effective in analyzing waves. What has struck me most about this approach is how I can use the same analytic framework to do predictions as well as to manipulate experimental data. As an experimentalist, I had found it very frustrating having my analytical tools incompatible with my experiments. For example, it is experimentally impos sible to generate a step-function wave and yet that is the type of analytical solution available. Spectral analysis is very encompassing - it touches on analysis, numerical meth ods, and experimental methods. I wanted this book to do justice to its versatility, so many subjects are introduced. As a result some areas may seem a little thin and I regret this. But I do hope, nonetheless, that the bigger picture, the unity, comes across. To encourage you to try the spectral analysis approach I have included complete source code listings to some of the computer programs mentioned in the text.
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