A plate-beam model of sound transmission through an orthogonally stiffened plate

To analyze the sound transmission problem of an orthogonally stiffened plate,a theoretical model is developed based on the classical theory of vibration of thin plate and beam.Firstly,the reaction forces and moments are obtained at the line connections between the plate and stiffeners by analyzing the forced bending and torsional motion of the stiffeners,and are incorporated to the governing equation of vibration of the plate,yielding a vibro-acoustic equation that describes the coupling of sound waves and the plate structure.By solving this equation,the Transmission Loss (TL) formulation is derived using the space harmonic expansion method.Then,the sound insulation effects of an infinite plate and a single periodically stiffened plate are studied,and a comparison with existing results validates our theoretical model.Finally,we investigate the influence of distribution of stiffeners on the sound isolation effect of the orthogonally stiffened plate,and show that the induced TL dips can be effectively avoided by a proper design of the distribution form of stiffeners.