Analytical sensitivity of acoustic power radiated from plates

A general formulation to obtain the analytical expressions for the sensitivity of the acoustic power radiated by a vibrating structure to one of its design variables is described. The formulation, which is based on finite elements, is applied to both single frequency and broad band harmonic excitation of plates. The sensitivity coefficients indicate the effect of changing various design or modeling parameters on the acoustic power and can be used to optimize the structure for minimum sound radiation. Analytical sensitivity estimates are compared with finite difference values. Results show that analytical sensitivity analysis is important from both computational time and accuracy points of view.