A general formulation to obtain the analytical expressions for the sen
sitivity of the acoustic power radiated by a vibrating structure to on
e of its design variables is described. The formulation, which is base
d on finite elements, is applied to both single frequency and broad ba
nd harmonic excitation of plates. The sensitivity coefficients indicat
e the effect of changing various design or modeling parameters on the
acoustic power and can be used to optimize the structure for minimum s
ound radiation. Analytical sensitivity estimates are compared with fin
ite difference values. Results show that analytical sensitivity analys
is is important from both computational time and accuracy points of vi
ew.