Material tailoring of structures to achieve a minimum radiation condition

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 condition. This particular velocity distribution is referred to as the "weak radiator" velocity profile. 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. In the first step, a finite element adaptation of the integral wave equation is combined with the Lagrange multiplier theorem to obtain a surface velocity distribution that minimizes the radiated sound power. In the second step, extensive use of structural finite element modeling as well as linear programming techniques is made. 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 three important characteristics. First, the weak radiator structure shows lower vibration amplitude near its boundaries. Second, the weak radiator structure exhibits lower wave number content in the supersonic region. Third, the distribution of surface acoustic intensity on the weak radiator structure is very small at all the points along its surface. The effect of modal overlap on the performance of the weak radiator structures is found to be negligible. While the method employed here is general, the example of a simple beam radiating in a rigid baffle is used for the purpose of illustration.

Experimental Verification of Structural-Acoustic Modelling and Design Optimization

“…In that example, the "rst eigenfrequency of an engine cover plate was decreased while the radiated noise level was reduced by about 12 dB. Similar investigations [17] were reported for piecewise constant material data like Young's modulus or density. Reductions between 2 and 23 dB were achieved.…”

A general optimization strategy for sound power minimization

“…Shape optimization has been shown to be effective by Bernard (1985) and Wilcox and Lalor (1987). More recent work in this area has been carried out by Lamancusa (1988), Sivakumar et al (1991) and Naghshineh et al (1992).…”

Optimisation of the structural modes of automotive-type panels using line stiffeners and point masses to achieve weak acoustic radiation

“…An alternative to this would be to calculate the optimum modal weight vector from a purely acoustic optimisation procedure, as described by Naghshineh et al in Ref. [14] and then try to adjust the structural parameters in order to obtain the desired modal weight vector. However, one of the problems with this approach is that matching the calculated modal weight vector with the desired modal weight vector cannot be achieved perfectly under all constraint mass and stiffener conditions.…”