有限元与声辐射模态的薄板声辐射灵敏度分析

采用有限元与声辐射模态方法研究了薄板声辐射的灵敏度。应用有限元方法求出结构的速度分布后，利用Rayleigh积分求出薄板的声压，然后将薄板的声辐射功率表示为薄板速度分布的正定厄米特二次型；将薄板的声辐射功率对设计变量求偏导，薄板声辐射的灵敏度转化为阻抗矩阵的灵敏度与速度分布的灵敏度，最后通过声辐射模态理论和有限元方法可以分别求出结构阻抗矩阵的灵敏度与速度分布的灵敏度。以四边简支的薄板作为数值算例，对所提出的方法进行了验证。

Acoustic sensitivity analysis of thin plate by using FEM and sound radiation mode method

In this paper, the sound radiation sensitivity of thin plate is studied by using FEM and sound radiation mode method. The velocity distribution of structure is solved by FEM and the surface sound pressure is computed by Rayleigh integral respectively. Then, the sound power can be expressed as a positive definite and Hermitian. Finally, the sound radiation sensitivity can be expressed as sensitivities of the impedance matrix and the velocity of plate by derivation of sound radiation power with respect to design variables, which can be solved by sound radiation mode theory and FEM. Taken a simple supported thin plate as a simulation example, the simulation results show the validity of the presented method.