By C.M. Linton, P. McIver
Even if a variety of mathematical recommendations can observe to fixing difficulties regarding the interplay of waves with constructions, few texts speak about these innovations inside that context-most usually they're awarded irrespective of any purposes. guide of Mathematical concepts for Wave/Structure Interactions brings jointly probably the most vital strategies necessary to utilized mathematicians and engineers.Each bankruptcy is devoted to a specific approach, equivalent to eigenfunction expansions, multipoles, critical equations, and Wiener-Hopf equipment. different chapters speak about approximation ideas and variational equipment. The authors describe all the options by way of wave/structure interactions, with so much illustrated via software to investigate difficulties. they supply certain reasons of the real steps in the mathematical improvement, and, the place attainable, actual interpretations of mathematical effects. guide of Mathematical strategies for Wave/Structure Interactions successfully bridges the distance among the heavy computational equipment most well liked by way of a few engineers and the extra mathematical method favourite through others. those thoughts offer a robust technique of facing wave/structure interactions, are with no trouble utilized to correct difficulties, and light up these difficulties in a fashion that neither a in basic terms computational technique nor a immediately theoretical remedy can.
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Extra resources for Handbook of mathematical techniques for wavestructure interactions
A system of equations which converges much more rapidly can be derived, however. This is because the semi-inﬁnite dock problem (where the dock occupies x > 0, z = 0) can be solved explicitly (as will be demonstrated in Chapter 5). 139) n ≥ 1. 140) The sum over n in this system still converges like 1/n2 , but rather than truncate this system of complex equations and solve it numerically we can take advantage of the fact that the terms exp(−2βm a) all tend to zero rapidly as a/h gets large and that if the exponential terms were not present the system could be solved explicitly.
A diﬀerent form for the solution of the radiation problem involving an integral representation was given by McIver (1994b). In the context of acoustics the history of the problem described in this section goes back to the 19th century with the work of Lord Rayleigh in 1878 on the interaction of sound waves with cylinders whose diameter is small compared to wavelength (Rayleigh 1945, §343). 1 below. 5 Matched eigenfunction expansions There are very few geometries for which the solution can be written in the form of a single eigenfunction expansion as in the previous section.
54) The reduction of a problem posed over the whole range x ∈ (−∞, ∞) to two problems each posed on x < 0 often leads to a considerable saving of eﬀort. 16) through x = r cos θ and y = r sin θ. 3) for W(r, θ) ≡ W (x, y) is 1 ∂ r ∂r © 2001 By CRC Press LLC r ∂W ∂r + 1 ∂2W = kn2 W. 58) say. 59) for some constants A and B. In many applications, for example those involving a ﬂuid domain exterior to a ﬁnite structure, the requirement that the potential be continuous implies that β must be an integer, m, say.
Handbook of mathematical techniques for wavestructure interactions by C.M. Linton, P. McIver