Efficient semi-analytical methods for the vibration response of and acoustic radiation from a periodical orthogonally rib-stiffened plate

For performing a more reasonable theoretical forecasting and analysis of the vibration response and acoustic radiation characteristics of an infinite plate, which is stimulated by an harmonic plane pressure and stiffened by two periodical sets of orthogonal ribs, corresponding mathematical models are respectively established. Combined the technique of Fourier transforms, Poisson summation equations and space harmonic method, the vibration response and acoustic radiation pressure of the rib-stiffened plate are expressed as functions of infinite sets of displacement harmonic amplitudes, and then corresponding efficient solving methods are proposed and approximate solutions for finite terms of the harmonic amplitudes are also provided by employing the truncation technique. The validity of the proposed methods is verified and the effects of the vibration response, rib spacing and torsional moment of the ribs on the radiation pressure are also examined. Theoretical results indicate that the modal frequencies of the stiffened plate can be affected by the torsional moment of the ribs, which thus can not be neglected for engineering applications of high precision. By adjusting rib spacing and cross section area of the ribs, the far field radiation pressure of the plate can be reduced by the attachment of the ribs in the low frequency range.