Structural-acoustic sensitivity analysis for optimization of shell geometry with respect to lower noise emission

Passive reduction of sound emission for vibrating components became more and more attractive because of enhanced computer systems in the last years. For thin radiating structures optimally shaped shell geometries represent a concept that applies local curvature dependent stiffening. The acoustic property of interest (the objective function) is usually the sound pressure at a certain internal field point for cavity problems. For investigation of sound emission into air a one-directional fluid-structure coupling is considered to be sufficient. Thus, for calculation of structural vibration FEA is applied and the acoustic field is evaluated by the boundary-element method using the surface velocities of the vibrating structure as further boundary condition. To provide a more general criterion of the acoustic behavior a relatively large frequency range consisting of more than one hundred structural modes is investigated. The objective function will usually be an average of the noise transfer function over this range. According to this, computation of objective function and furthermore sensitivity analysis become rather expensive and a low number of calculations of the objective function is worth striving for. Here the adjoint method is used to provide structural sensitivities, where the adjoint loads are computed via semi-analytical sensitivity analysis of the elemental matrices of the structural model. The acoustic sensitivities for sound pressure with respect to the velocity distribution of the surface are calculated by computing the acoustic transfer vectors or acoustic influence coefficients, respectively. This assumes that the fluid is neglectably changed by modification of the structure, i.e. the structural modification is much smaller than the acoustic wave length.