Damping design of harmonically excited flexible structures with graded materials to minimize sound pressure and radiation

Topology optimization is an effective method in the design of acoustic media. This article presents optimization for graded damping materials to minimize sound pressure at a reference point or sound power radiation under harmonic excitation. The Helmholtz integral equation is used to calculate an acoustic field to satisfy the Sommerfeld conditions. The equation of motion is solved using a unit dynamic load method. Formulations for the sound pressure or sound power radiation in an integral form are derived in terms of mutual kinetic and strain energy densities. These integrals lead to novel physical response functions for solving the proposed optimization problem to design graded damping materials. The response function derived for individual frequency is utilized to solve the multi-objective optimization problem of minimizing sound pressure at the reference point for excitations with a range of frequencies. Numerical examples are presented to verify the efficiency of the present formulations.