双周期加筋微穿孔板的振动响应及声透射的研究

本文主要研究了水下无穷大双周期加筋微穿孔薄板，在平面声波斜入射下的振动响应和声透射，并提出了一种半解析半数值的计算方法。利用微穿孔板的声阻抗以及薄板表面的振速边界条件，建立了加筋穿孔薄板的振动方程，并根据傅立叶变换及空间波数法将振动位移表达为波数分量的迭加形式。采用数值计算的方法对波数分量进行求解并通过傅里叶逆变换，最终得到了双周期加筋穿孔薄板的振动响应及透射系数。通过与Takahashi穿孔板声压结果的对比，证明了本方法的正确性。在算例中，分析了加强筋及穿孔率对薄板结构的振动和声透射的影响。

INVESTIGATION OF THE VIBRATION RESPONSE AND SOUND TRANSMISSON OF A MICRO-PERFORATED PLATE PERIODICALLY STIFFENED BY TWO SETS OF ORTHOGONAL BEAMS

A semi-analytical method to estimate the vibration response and sound transmission of an infinite micro-perforated plate,stiffened by two periodic sets of orthogonal beams,is proposed in this paper.The plate is submerged in water fluid and excited by a plane wave at arbitrary angle of incidence.Based on the velocity boundary condition and acoustic impedance of the micro-perforated plate,the equation of the vibration response of the studied structure is established,which is then expressed in terms of an infinite set of space harmonic amplitudes using the Fourier transforms and space harmonic method.After solving these space harmonic amplitudes numerically,the vibration response and sound transmission coefficient of the perforated plate in the physical space are finally obtained by employing the Fourier inverse transform.Comparisons with sound pressure results of the unstiffened perforated plate of Takahashi illustrate the validity of the proposed approach.In numerical examples,effects of the perforation ratio and periodic beams on the vibration response and acoustic transmission coefficient are investigated.