Material tailoring of structures to achieve a minimum radiation efficiency

Abstract

A strategy is developed for designing structures that radiate sound inefficiently in light fluids. The problem is broken into two steps. First, given a frequency and overall geometry of the structure, a surface velocity distribution is found that produces a minimum radiation efficiency. This particular velocity distribution is referred to as the ‘‘weak radiator’’ velocity profile. A finite element adaptation of the integral wave equation is combined with the Lagrange multiplier theorem to obtain this surface velocity distribution. Second, a distribution of Young’s modulus and density distribution is found for the structure such that it exhibits the weak radiator velocity profile as one of its mode shapes. Extensive use of structural finite element modeling as well as linear programming techniques is made to find this distribution. The result is a weak radiator structure. When compared to a structure with uniform material properties, the weak radiator structural response is found to exhibit lower wave-number content in the supersonic region. The effect of modal overlap on the performance of the weak radiator structures is found to be negligible. The example of a simple beam radiating in a rigid baffle is used for the purpose of illustration.