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The focus of this article is on shape and topology optimization of transientvibroacoustic problems. The main contribution is a transient problemformulation that enables optimization over wide ranges of frequencies withcomplex signals, which are often of interest in industry. The work employs timedomain methods to realize wide band optimization in the frequency domain. Tothis end, the objective function is defined in frequency domain where thefrequency response of the system is obtained through a fast Fourier transform(FFT) algorithm on the transient response of the system. The work utilizes aparametric level set approach to implicitly define the geometry in which thezero level describes the interface between acoustic and structural domains. Acut element method is used to capture the geometry on a fixed background meshthrough utilization of a special integration scheme that accurately resolvesthe interface. This allows for accurate solutions to strongly coupledvibroacoustic systems without having to re-mesh at each design update. Thepresent work relies on efficient gradient based optimizers where the discreteadjoint method is used to calculate the sensitivities of objective andconstraint functions. A thorough explanation of the consistent sensitivitycalculation is given involving the FFT operation needed to define the objectivefunction in frequency domain. Finally, the developed framework is applied tovarious vibroacoustic filter designs and the optimization results are verifiedusing commercial finite element software with a steady state time-harmonicformulation.

Topology optimization of transient vibroacoustic problems for broadband filter design using cut elements