正交加筋板声透射的板梁理论模型研究

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

为了研究正交加筋板的声透射问题,基于经典薄板和梁振动理论,建立了正交加筋板声透射的板梁理论模型。首先通过分析加强筋的受迫弯曲和扭转运动,求得了平板和加强筋线接触之间的反力和反力矩,然后将其引入到平板振动控制方程中,得到了正交加筋板声振方程,最后采用空间谐波展开法求解该方程得到了传声损失的表达式;在此基础上,首先研究了无限大平板和单向加筋的隔声性能,通过与解析解及两种简化模型的计算结果作对比,验证了所建理论模型的有效性;并进一步研究了加筋形式对正交加筋板隔声性能的影响。结果表明:选择合适的加筋形式可以有效避开结构的隔声波谷。

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 axe 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 orthogonafly stiffened plate, and show that the induced TL dips can be effectively avoided by a proper design of the distribution form of stiffeners.