Sound radiation by baffled and constrained plates

ISSN： 0022-460X

Source： Journal of Sound and Vibration, Vol.179, Iss.1, 1995-01, pp. : 63-77

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Abstract

The coupling between the acoustic waves in a half-space above a thin plate and the vibration of the plate is studied. For the sake of simplicity, the geometry is such that the problem considered is two-dimensional. The plate equation is then reduced to a beam equation. Two different problems are considered: the baffled plate, which is free to vibrate within a finite region but is rigidly clamped outside this region; and the constrained plate, which is free to vibrate both within and outside the finite region but is constrained (clamped) on the boundary between them. In each case the plate is excited by a harmonic force located in the finite region and then radiates an acoustic wave. Four topics are considered. First, a formulation and a numerical solution, obtained by using a simple boundary element method (the collocation method), of a boundary integral equation for the baffled plate case is presented. Secondly, an analytical method for the constrained case is developed. Comparison of the plate displacement in the two cases shows that the displacement of the baffled plate can be approximated by that of the constrained plate, restricted to the domain limited by the constraints. Then, formulae for the far acoustic field behaviour of the constrained plate and for the exact and approximate (deduced from the constrained case) solutions for the baffled plate are presented. Numerical examples show that, in the case treated here (a steel plate in contact with water), the exact solution and the approximate one are in agreement.