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

ISBN-10: 3540555625

ISBN-13: 9783540555629

ISBN-10: 3642517277

ISBN-13: 9783642517273

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 crucial equation over the constitution floor. even if, the classical boundary imperative equation formulations of this challenge both don't have any suggestions or do not need distinctive recommendations at convinced attribute frequencies (which depend upon the skin geometry) and it's important to hire changed boundary essential equation formulations that are legitimate for all frequencies. the actual strategy followed the following comprises an arbitrary coupling parameter and the impression that this parameter has at the balance and accuracy of the numerical technique used to unravel the quintessential equation is tested. The boundary imperative 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 query is resolved by means of demonstrating that .the method to the coupled challenge isn't designated on the attribute frequencies and that it will be significant to hire an vital equation formula legitimate for all frequencies.

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**Extra resources for Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid-Structure Interaction Problem**

**Example text**

20 ,, ,: CD ::::I! ;::) Z Z 0 15 E 0 z 8 10 5 . , ,, . 4' ___ -.. " ~.... ". if. W __ -"8~" ~ '@I----. ~. ~. 9: Condition number of the direct formulation for a unit sphere with v(p, k) zero over different numbers of elements. , 20 CD ::::I! ;::) Z Z 0 ," 15 0 z 0 U . " :' I' . I' . •... •.. 3717 o ~::'~~:t~J_ • ~:7~,~~~9. 8, with v(p, k) zero over different numbers of elements. 4. 5 Numerical Results Exact solutions in closed form, usually as infinite series of slowly converging wave functions, can only be obtained in special cases [96].

15) for solving the exterior Helmholtz problem is known as the T-matrix method [135]. 4, when discussing the conditioning of the boundary integral equation of Burton and Miller with respect to the coupling parameter o. 3 Projection Methods The methods most commonly used to solve boundary integral equations are the projection methods. Let X be a normed linear space and let Xn be a sub-space of X spanned by the basis functions {1/h, t/;2,' .. ,t/;n}. Let 'Pn be a projection operator from X onto X n, that is 'Pn4> = 4> for all 4> E X n.

5 Numerical Results Exact solutions in closed form, usually as infinite series of slowly converging wave functions, can only be obtained in special cases [96]. However, exact solutions can be generated for problems which are equivalent to those having acoustic point sources in the interior region D_ [4, 59]. The acoustic pressure at a point P E R3 generated by a set of point sources at qj E D_ with strengths A j , j = 1,2, ... , Q, in the absence of the structure, is given by Q ¢>(p) = LAj j=1 eiklp-qjl 4' P - ,.

### Coupled Boundary and Finite Element Methods for the Solution of the Dynamic Fluid-Structure Interaction Problem by Dr. Siamak Amini, Dr. Paul John Harris, Dr. David T. Wilton (auth.)

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