  The focus of this article is on shape and topology optimization of transient
vibroacoustic problems. The main contribution is a transient problem
formulation that enables optimization over wide ranges of frequencies with
complex signals, which are often of interest in industry. The work employs time
domain methods to realize wide band optimization in the frequency domain. To
this end, the objective function is defined in frequency domain where the
frequency response of the system is obtained through a fast Fourier transform
(FFT) algorithm on the transient response of the system. The work utilizes a
parametric level set approach to implicitly define the geometry in which the
zero level describes the interface between acoustic and structural domains. A
cut element method is used to capture the geometry on a fixed background mesh
through utilization of a special integration scheme that accurately resolves
the interface. This allows for accurate solutions to strongly coupled
vibroacoustic systems without having to re-mesh at each design update. The
present work relies on efficient gradient based optimizers where the discrete
adjoint method is used to calculate the sensitivities of objective and
constraint functions. A thorough explanation of the consistent sensitivity
calculation is given involving the FFT operation needed to define the objective
function in frequency domain. Finally, the developed framework is applied to
various vibroacoustic filter designs and the optimization results are verified
using commercial finite element software with a steady state time-harmonic
formulation.
