جفت سازی FEM-BEMو تجزیه و تحلیل حساسیت ساختاری صوتی برای هندسه پوسته

Passive noise control by modification of structural geometry moves more and more into the field of vision for designers. This structural–acoustic optimization shows high potential in minimization of radiated noise especially for thin shell geometries. Since computer systems have been enhanced dramatically in recent years numerical simulation of structural vibration and acoustic field was accelerated significantly. But still the sensitivity analysis represents the bottle neck in computational efforts of gradient-based optimization. Furthermore, the coupling between FE and BE analysis in structural–acoustic simulation of large scale models will occur as an additional challenge because of non-matching meshes. In this paper, a fast method for computation of sensitivities of acoustic properties with respect to shell geometry is presented. Therefore, a concept to parameterize the structural geometry is explained. Additionally, the coupling procedure is simplified to reduce computational effort. Finally, this method is applied to an academic example. The sensitivity of the sound pressure at an internal point of an oblique box is investigated, when one side of this six-sided box is geometrically modified.

Since acoustic properties of components became an additional challenge in design, efficient techniques may be sought within numerical optimization processes. Due to improved computational capabilities in recent years the simulation of acoustic fields in accordance to vibrating and thus sound radiating structures has significantly accelerated. An acoustic property can be minimized by modifying design variables of the structure during the optimization. Marburg [1] presents an overview of the current state-of-the-art in structural–acoustic optimization. Furthermore, structural–acoustic sensitivities with respect to design variables are most expensively computed in gradient-based optimization. Often, these sensitivities are approximated using global finite-difference schemes for the objective function, cf. Lamancusa [2], Christensen et al. [3], Marburg and Hardtke [4]. This method requires at least one additional computation of objective function for each design parameter. To overcome this problem, semi-analytical or even analytical sensitivity analysis appears more appropriate. Thus, adjoint variable methods as in Choi et al. [5] and [6] or Wang et al. [7] and [8] can be implemented. Generally, these applications need to compute the acoustic field for each design step. By simplifying the fluid–structure coupling to a purely structure-induced noise the acoustic model is supposedly negligibly changed by structural modification. This is suitable for structures being more dense than the fluid. This approach represents the structural dynamic behavior in vacuum followed by a post-processing step to evaluate the acoustic properties. The acoustic sensitivity with respect to surface velocity used in this method may be termed as influence coefficients, cf. Ishiyama et al. [9], Marburg [10], or recently as acoustic transfer vectors [11]. Usually, structural frequency response is calculated for broad frequency ranges by FEA using mode superposition techniques. To prevent discretizing the three-dimensional fluid, we carry out a boundary element analysis to compute sound pressures at internal points of the cavity. These two methods do not necessarily need to be applied on the same mesh. Thus, a coupling procedure must correlate structure to fluid mesh and vice versa. Parameterizing the geometric modification of the shell structure will reduce the number of design variables and the optimization procedure becomes more manageable. All these concepts are applied in an example of an oblique six-sided box to avoid effects by symmetry. Herein the sound pressure at an internal point of the box is optimized by modifying one side of the box using a spline parameterization concept.

In this paper a method has been presented to compute structural–acoustic sensitivities of geometrically modified shells efficiently. The geometrical modification was parameterized to achieve a small number of design variables by simultaneously keeping the variety of new design shapes broad. By assuming the coupling between structure and fluid to be uni-directional, we neglect excitation of the structure by the fluid. This allows us to formulate the sound pressure at internal points in terms of normal velocity at the structure’s surface without to compute the acoustic field at each design step. This improvement is usable in sensitivity analysis such that the acoustic sensitivity of an internal point can be separated into partial sensitivities. Thus, the storage and computational cost is reduced by preprocessing the acoustic and parametric sensitivity and involving these into the structural sensitivity at each design step. This method was carried out and presented on an academic example of an oblique box for parametric studies.