By James F. Doyle
The examine of wave propagation turns out very distant to many engineers, even to people who are taken with structural dynamics. i feel one of many purposes for this can be that the examples often taught in class have been both as simple as to be inapplicable to actual global difficulties, or so mathematically abstruse as to be intractable. This e-book includes an method, spectral research, that i've got came across to be very powerful in studying waves. What has struck me so much approximately this technique is how i will use a similar analytic framework to do predictions in addition to to control experimental information. As an experimentalist, I had came upon it very not easy having my analytical instruments incompatible with my experiments. for instance, it's experimentally impos sible to generate a step-function wave and but that's the kind of analytical resolution on hand. Spectral research is particularly encompassing - it touches on research, numerical meth ods, and experimental tools. i needed this e-book to do justice to its versatility, such a lot of topics are brought. consequently a few components could seem a bit skinny and that i remorse this. yet I do wish, still, that the larger photo, the cohesion, comes throughout. To inspire you to attempt the spectral research strategy i've got incorporated whole resource code listings to a few of the pc courses pointed out within the text.
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Additional info for Wave Propagation in Structures: An FFT-Based Spectral Analysis Methodology
This is valid even though the solution itself may not be of the exponential form (as in the Bessel solution, for instance). Thus it will be sufficient to study superpositions of this form. Phase Speed At a typical frequency, the wavenumber can be written in terms of its real and imaginary parts as giving the wave in the form u(x, t) = E Fn e-kIZe-·(kRz-wt) This is recognized as having three parts: an amplitude spectrum Fn , a spatially decaying term e- kI "', and the propagating sinusoids e-·(kR",-wt).
200. 5: Transform of a modulated pulse with q = 50 kHz and a = 50ILS. It is apparent what is happening. 4). The product of the two in the time domain is a convolution in the frequency domain. The convolution tends to distribute the effect of the pulse. ) Otherwise, it will appear broad-banded. 8 Sampled Waveforms By necessity, real-signal records are finite in length, and this can add other problems to the scheme of estimating its spectral content. This section reviews the major effects that should be considered.
In that case, the computations are on the order of NS. The purpose of the FFT is to take advantage of the special form of the exponential terms to reduce the number of computations to even less than N2. Repeated Patterns The key to understanding the FFT algorithm lies in seeing the repeated forms of numbers. This will be motivated by considering the special cases of N being 4 and 8. First consider the matrix of the exponents -i21f(~) -i21f N 0 0 0 0 0 0 1 2 3 2 4 6 3 6 9 0 0 (N -1) 2(N - 1) 3(N -1) 0 (N -1) 2(N - 1) 3(N - 1) (N -1)(N -1) It is apparent that for an arbitrary value of N, 21f will be multiplied by non-integer numbers (in general).