Abstract
The calculation of vibrational responses of complex systems on frequency bands appears to be more and more important in engineering simulation. This is particularly true in the medium frequency regime where the solution is very sensitive to the frequency. In this work, we propose a new path to determine the frequency response of a system at many frequencies. It is based on the Variational Theory of Complex Rays (VTCR)[1], a mid frequency dedicated numerical strategy, and the Proper Generalized Decomposition (PGD) [2], a model order reduction technique. The VTCR enables one to model the problem thanks to the use of waves, and the PGD expands the VTCR approximation over the frequency band through a separated variable representation. This strategy is illustrated on a 2-D acoustic car cavity example.
Highlights
The prediction of the frequency responses of complex systems in frequency bands is required in many industrial applications, like car or aerospace acoustics
It is based on a combination of the variational theory of complex rays (VTCR), used to find the solution of the vibration problem at a fixed frequency, and the proper generalized decomposition (PGD), used to find the best separated variable representation of this solution over a frequency band
We proposed here a new path for solving vibration problems on frequency bands
Summary
The prediction of the frequency responses of complex systems in frequency bands is required in many industrial applications, like car or aerospace acoustics. The definition of advanced numerical strategies for predicting the acoustic response of complex systems in the midfrequency ranges is the subject of this work It uses the combination of the variational theory of complex rays (VTCR) [1] and the proper generalized decomposition (PGD) [2]. We propose a new path to determine the frequency response of a system at many frequencies It is based on a combination of the VTCR, used to find the solution of the vibration problem at a fixed frequency, and the PGD, used to find the best separated variable representation of this solution over a frequency band. A 2-D numerical illustration on a car cavity is proposed to see the benefits of such an approach
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