A design sensitivity analysis of high frequency structural-acoustic problem is formulated and presented. The Energy Finite Element Method (EFEM) is used to predict the structural-acoustic responses in high frequency range, where the coupling between the structural and acoustic domain are modeled by using radiation efficiency. The continuum design sensitivity formulation is derived from the governing equation of EFEM and the discrete method is applied in the variation of the structural-acoustic coupling matrix. The direct differentiation and adjoint variable method are both developed for the sensitivity analysis, where the difficulty of the adjoint variable method is overcome by solving a transposed system equation. Parametric design variables such as panel thickness and material damping are considered for sensitivity analysis, and the numerical sensitivity results show excellent agreement comparing with the finite difference results.

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