This paper deals with the sensitivity analysis of structural acoustic performance in presence of non-proportional damping and optimal layout design of the damping layer of vibrating shell structures under harmonic excitations. The structural system with a partially-covered damping layer has a non-proportional global damping matrix. Therefore, the method of complex mode superposition in the state space is employed in the dynamic response analysis. The sound pressure is calculated with the structural response solution by using the boundary element method. In this context, an adjoint variable scheme for the design sensitivity analysis of sound pressure is developed. In the optimal design problem, the design objective is to minimize the structural vibration-induced sound pressure at a specified point in the acoustic medium by distributing a given amount of damping material. An artificial damping material model that has a similar form as in the SIMP approach is employed, and the relative densities of the damping material are considered as design variables. Numerical examples are given to illustrate the validity and efficiency of this approach. The influences of the excitation frequency, the damping coefficients and the locations of the reference point on the optimal topologies are also discussed.
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