A semi-analytical method for the vibration of and sound radiation from a two-dimentional beam-stiffened plate

A semi-analytical method based on space harmonics to investigate the vibration of and sound radiation from an infinite, fluid-loaded plate is presented. The plate is reinforced with two sets of orthogonally and equally spaced beam stiffeners, which are assumed to be line forces. The response of the stiffened plate to a convected harmonic pressure in the wave-number space is obtained by adopting the Greenʹs function and Fourier transform methods. Using the boundary conditions and space harmonic method, we establish the relationship between the stiffener forces and the vibration displacement of the plate. In this paper, the stiffener forces are expressed in terms of harmonic amplitudes of the plate displacement, which are calculated by using a numerical reduction technique. Finally, the Fourier inverse transform is employed to find expressions of the vibration and sound radiation in physical space. Agreements with existing results prove the validity of this approach and more numerical results are presented to show that this method converges rapidly.