高效半解析方法分析周期正交加筋板的振动-声辐射特性

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

为了对水下无穷大双周期正交加筋板结构模型在简谐面力激励下的振动响应及声辐射特性进行更为合理的理论预测与分析,建立了加筋板结构的数学模型。结合傅里叶变换、泊松迭加公式及空间波数法,将周期加筋板的振动响应及辐射声压表达为关于结构位移谐波分量的函数方程,对加筋板模型提出了高效分析求解方法并进行了谐波分量截断求解。验证了方法的正确性,并分析了结构的振动特性以及加强筋周期间距和扭矩对辐射声压的影响。结果表明,加强筋的扭转作用影响加筋板结构的振动模态频率,对于较高精度要求的工程应用,加强筋的扭转作用不能忽略。通过调节加强筋周期间距及横截面尺寸,可以降低薄板在较低频域区间的远场辐射声压。

For performing a more reasonable theoretical forecasting and analysis of the vibration response and acous- tic 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 affectedby 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.