The purpose of this research is to design optimal boundary supports for minimum structural sound radiation. The influence of the boundary conditions on the structural dynamics of a cantilever beam is first examined to motivate the research. The boundary supports constraining both the in- and out-of-plane degrees of freedom of the plate are considered as the design parameters. The fixed and free boundary degrees of freedom are represented by a continuous function with the help of homogenization. Analytical expressions of sensitivity functions are employed in the optimization, leading to more efficient and accurate numerical solutions. The sensitivity expressions are based on the linear equation system obtained with the finite element method. Numerical examples of single frequency and broadband optimizations are presented. The sensitivity of the optimal design parameters with respect to small random perturbations is also studied. The examples demonstrate that an encouraging reduction of sound radiation as measured by the mean square normal velocity can be achieved with the optimal boundary conditions as compared with the base line structure.

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