ON THE RESONANCE OF ACOUSTIC-WAVES IN SLIGHTLY DEFORMED AND SLOWLY MOVING SLABS

The stability is studied of acoustic waves generated by a time harmonic force in slabs described by: 0 less than or equal to z less than or equal to 1 +/- epsilon g(x,y). By using a recently developed method, the exact solution of the Dirichlet problem is found for epsilon = 0. It is shown that the solution is unstable against values of the frequency: omega = n pi, n epsilon N. This is in agreement with the result already known in the literature, but found by other means. In a slightly deformed slab, 0 < epsilon much less than 1,it is shown that stabilization of the resonant wave occurs at a time of order omega epsilon(-1/2). This is valid if the upper boundary is a concave surface. In case of a slab with slowly moving upper boundary, only the growth rate of the amplitude of the resonant wave is reduced. This holds for a non-oscillating motion of the upper boundary. In the case of an oscillating motion a further resonance is produced.