Acoustic Design Sensitivity for Structural Radiators

An analysis technique designated as acoustic design sensitivity (ADS) analysis is developed via the numerical treatment of a discrete quadratic expression for the total acoustic power radiated by a three-dimensional extended structure. A boundary element formulation of the Helmholtz Integral Equation is the basis of the analysis leading to the quadratic power expression. Partial differentiation of the quadratic power expression with respect to a known surface velocity distribution leads to a sensitivity distribution, represented by a distribution of values on the surface of a structure. The sensitivity values represent a linear approximation to the change in the total radiated power caused by changes in the surface velocity distribution. For a structure vibrating with some portions of its surface rigid and such that the acoustic wavelength is long compared to a characteristic dimension of the structure, ADS analysis reveals that the rigid surfaces strongly influence the sensitivity distribution, as expected. Under such conditions, the rigid surfaces can exhibit the maximum value of the entire sensitivity distribution, even though the acoustic intensity is identically zero on a rigid surface. As the frequency increases, and the acoustic wavelength becomes comparable to a characteristic dimension of the structure, the position of the maximum value of the sensitivity distribution will coincide with the region of the maximum surface acoustic intensity.