×

Uniformly accurate expressions for sound waves induced by a vibrating planar boundary. (English) Zbl 0733.76066

Summary: The antecedent of this investigation [ibid. 73, No.3, 129-133 (1991)] derived a perturbation description of the velocity potential for two- dimensional finite acoustic waves induced by the vibration of a region in a planar boundary. Those results, which used a complex Fourier transform to represent the dependence on the transverse position, lacked uniform validity in the propagation distance from the boundary. Expressions for the acoustic pressure and velocity components derived from the potential function have the same behaviour. The current analysis employs a coordinate straining transformation to correct the irregularities in the acoustic pressure and fluid velocity components, and thereby obtain uniformly accurate expressions. Then the strained coordinate transformation is eliminated by a Fourier analysis and a Bessel-Fubini type expansion is derived instead, which improves the computational efficiency by several orders of magnitude. A quantitative example which depicts various spatial and temporal responses is cited.

MSC:

76Q05 Hydro- and aero-acoustics
42A38 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
PDFBibTeX XMLCite