Scattering of sound by a fluid-loaded plate with a distributed mass inhomogeneity

Abstract

The scattering of a plane acoustic wave by a fluid-loaded, thin, elastic plate, of infinite extent, with a distributed mass inhomogeneity is investigated. Two approaches are presented, an iterative approach valid when a measure of the distributed impedance is much lower than that of the uniform fluid-loaded plate, and a full numerical solution which while having no restricting assumptions is somewhat demanding computationally. For the iterative solution a set of correction terms is evaluated and applied to the response of the uniform plate with no inhomogeneities. The number of correction terms required is dependent on the relative magnitude of the inhomogeneity. In the full numerical solution, the presence of the distributed inhomogeneity in the equation of motion, when expressed in the wave-number domain, results in a Fredholm integral equation of the third kind. By substituting for the product of the response and the plate characteristic equation (impedance), the Fredholm integral of the third kind is reduced to a Fredholm integral of the second kind. The plate response in the spectral wave-number domain is obtained from the solution of the Fredholm integral. Inverse Fourier transforming the wave-number domain response function gives the spatial domain solution for the response. The hybrid numerical analytical approach [J. Acoust. Soc. Am. 95, 1998–2005 (1994)] is used to perform the inverse Fourier transform. The far-field scattered pressure is obtained from the spectral domain solution of the response. Response and scattered pressure results for distributed mass inhomogeneities, with different distribution functions, are presented and compared to the results for a line inhomogeneity.

Sound radiation from a fluid-loaded infinite plate with a patch

“…A wavenumber transformation of Eqs. (8) and (11) yields D b w 000 ðx À p ÞÀD 2 w 000 ðx þ p ÞþD 2 jkw 00 ðx þ p ÞÀD b jkw 00 ðx À p Þ þD 2 k 2 w 0 ðx þ p ÞÀD b k 2 w 0 ðx À p ÞþD b jk 3 wðx À p ÞÀD 2 jk 3 wðx þ p Þ þD 2 e jkL w 000 ðx À p þLÞÀD b e jkL w 000 ðx þ p þLÞ þD b jke jkL w 00 ðx þ p þLÞÀD 2 jke jkL w 00 ðx À p þLÞ þD b k 2 e jkL w 0 ðx þ p þLÞÀD 2 k 2 e jkL w 0 ðx À p þLÞ þD 2 jk 3 e jkL wðx À p þLÞÀD b jk 3 e jkL wðx þ p þLÞ…”

“…x p represents that x approaches x p from the lefthand side of the patch. Equations (8) and (11) of the displacement w(x) and surface sound pressure p(x, z ¼ 0) can be solved by wavenumber transformation. By applying the boundary conditions in Eq.…”

“…The most relevant work is found in two pioneering papers by Feit and Cuschieri,8,9 where they presented methods for and a physical understanding of the scattered sound by a fluid-loaded plate with a distributed mass or stiffness inhomogeneity. As the sound scattered by the plate is due to the sound radiation by the plate excited by the "blocked pressure" of the incident plane wave, their physical insights directly motivated work on sound radiation by a line-force driven fluid-loaded infinite plate with an attached finite elastic plate, which is the subject of this paper.…”

“…7 The dynamics of both the plate and patch are modeled by a classical thin plate theory for simplicity of analysis and a consistent comparison with the previous results. [1][2][3][4][7][8][9] For a more accurate description of the plate response in the higher frequency region, Mindlin plate theory is recommended. 10 The radiated sound power of the patched plate is examined to estimate the significance of the effects of the patch on the sound radiation and to raise questions and discussions about the mechanisms involved in the variations of sound power due to the patch.…”

Comparison of moments and couple-generating forces near discontinuities in structural-acoustic systems

“…It has been shown that the system response predicted using continuous substructure models can often differ from the predicted response when using discrete ͑i.e., lumped parameter͒ subsystems. 9,10 Other studies have considered how the scale, or geometric size, of a distributed feature impacts the response of a simple system. [11][12][13][14][15] Examples of attached substructures include a simple mass or a spring-mass subsystem.…”