湍流边界层作用下薄板随机振动声辐射的辛方法
摘要
The random sound radiation of thin plates subjected to turbulent boundary layer (TBL) excitations was studied in the symplectic duality system. Firstly, the cross power spectral density of the TBL was represented by a Fourier series, and the problem of the random sound radiation of structures excited by a random field was reduced to solve the deterministic response function, i.e. the structural response to a spatial and temporal harmonic pressure of unit magnitude. Secondly, the free vibration analysis of thin plates was introduced to the symplectic duality system, then a symplectic eigenproblem was formed with the method of separation of variables. Finally, the decoupled governing equations were derived through expansion of the response and excitation vectors in the symplectic space, to reduce the difficulty of solving the equations, and the symplectic analytical solution was obtained. In contrast to the modal decomposition method (MDM), the presented method is formulated in the symplectic duality system and does not need modal truncation, hence the computations are of high precision. In the numerical examples, the harmonic response functions for the thin plate were studied, and a comparison was made with the MDM to verify the effectiveness of the presented method. Thereafter, the sound pressure levels (SPL) of the power spectral density of the sound pressure response to the TBL were obtained, the convergence induced by the Fourier series expansions was examined, and the directivity functions of the radiation sound field were extensively investigated.