Coupled Boundary and Finite Element Methods for the Solution by Dr. Siamak Amini, Dr. Paul John Harris, Dr. David T. Wilton

By Dr. Siamak Amini, Dr. Paul John Harris, Dr. David T. Wilton (auth.)

This textual content considers the matter of the dynamic fluid-structure interplay among a finite elastic constitution and the acoustic box in an unbounded fluid-filled external area. the outside acoustic box is modelled via a boundary essential equation over the constitution floor. even if, the classical boundary indispensable equation formulations of this challenge both haven't any suggestions or should not have designated suggestions at convinced attribute frequencies (which rely on the outside geometry) and it will be significant to hire converted boundary fundamental equation formulations that are legitimate for all frequencies. the actual process followed the following includes an arbitrary coupling parameter and the impression that this parameter has at the balance and accuracy of the numerical procedure used to resolve the quintessential equation is tested. The boundary indispensable research of the outside acoustic challenge is coupled with a finite aspect research of the elastic constitution that allows you to examine the interplay among the dynamic behaviour of the constitution and the linked acoustic box. lately there was a few controversy over even if the coupled challenge additionally suffers from the non-uniqueness difficulties linked to the classical vital equation formulations of the outside acoustic challenge. this question is resolved by means of demonstrating that .the technique to the coupled challenge isn't designated on the attribute frequencies and that it is crucial to hire an fundamental equation formula legitimate for all frequencies.

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For the model problem of a sphere of radius a a general v(p, k) is considered. 104) as the S::"s are orthogonal on S. 15). 105) with S;;' gives 00 ik2a2E n E n=O m=-n O:nmh~(ka) [bnnbm",jn(ka) + ika:;;:j~(ka)l = AO:n", for n = 0,1, ... and in = -n, ... , 0, ... ,n. 108) A(nm)(nm) is the element of A in the row corresponding to (fl, m) and the column corresponding to (n, m). 107) will only give an approximation to the eigenvalues of the operator +Mk+ivNk since the infinite sums have been truncated.

90) where a prime denotes the derivative with respect to the argument. 94) with the corresponding 2n + 1 eigenvectors S::" m = -n, ... ,0, ... ,n. Clearly if ka is a zero of jn then + Mk has a zero eigenvalue and its null space is of dimension 2n + 1 (that is, the space spanned by S::" m = -n, ... ,0, ... ,n ). 15) for Gk(p, q); see [3J. The conditioning of the integral equations of interest will now be investigated. 10 that the operator + Mk + aNk has only a trivial null space for real k, provided the function a is such that I m( a(p, k)) is one-signed for all pES.

The numerical results presented here are for surfaces with the same typical dimension d. )2 + (~)2 = 1, d is given by d = 2a3+b. 50. For all of these surfaces d =1. Each of these surfaces was modelled using 15 linear axisymmetric boundary elements. 8 respectively, where v(p, k) = OPT denotes the choice of {VI, V2, ... , vn } which minimises the condition number. It is clear from these results that the near optimal choice is v(p, k) = II k for larger values of k, which is in agreement with the results of [3] and [77].

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