Energy balance for radiated waves and propagating vibration in a fluid-loaded beam under point excitation

Abstract

Using a compensating solution method [S. Kovinskaya and I. Krasnov, Acta Acust. 82, 237 (1996)] a field of flexural waves propagating along a submerged beam under a point excitation and a radiated acoustical field are represented analytically. The method is based on the Fourier integral transform of the vibration equation and is similar to the hybrid method [J. M. Cuschieri and D. Feit, J. Acoust. Soc. Am. 95, 1998–2005 (1994)]. The main and compensating solutions are determined as a result of the inverse Fourier transform along a real wave number axis of nonuniform and uniform equations, correspondingly. A sum of the main and compensating solutions must supply the vibration radiation condition. Let the last equation determine an indefinite coefficient in the compensating solution. The energy balance equation based on the solution of the problem leads to an energetic equivalence between a decreasing vibration and radiated spherical wave and the same between a cylindrical acoustical wave and an energy difference in the excitation point and infinity for propagating flexural wave.