Design sensitivity analysis and optimization of frequency averaged input power using the residue theorem

• The residue theorem is employed in the design optimization of a vibrating structure.
• The adjoint variable method is used for the design sensitivity computation.
• Numerical examples demonstrate the computational efficiency of the optimization scheme.
• High enhancement of the optimization process for the reduction of the radiated sound power.

The residue theorem is employed in the design optimization of the frequency averaged power injected into a linear second-order system. The dynamic behavior of a vibrating structure is obtained with the finite element method and the frequency averaged input power into the structure is adopted as an objective function. The design sensitivity with respect to each structural element is computed by the adjoint variable method with consideration for the residue theorem. The proposed method highly enhances the computational efficiency of the optimization and the design of the optimization leads to substantial reduction of the radiated sound power from the structure.