Finite and spectral cell method for wave propagation in heterogeneous materials |
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Authors: | Meysam Joulaian Sascha Duczek Ulrich Gabbert Alexander Düster |
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Affiliation: | 1. Numerical Structural Analysis with Application in Ship Technology, Hamburg University of Technology, Schwarzenbergstr. 95c, 21073, ?Hamburg, Germany 2. Faculty of Mechanical Engineering, Computational Mechanics, Otto-von-Guericke-University Magdeburg, Universit?tsplatz 2, 39106, ?Magdeburg, Germany
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Abstract: | In the current paper we present a fast, reliable technique for simulating wave propagation in complex structures made of heterogeneous materials. The proposed approach, the spectral cell method, is a combination of the finite cell method and the spectral element method that significantly lowers preprocessing and computational expenditure. The spectral cell method takes advantage of explicit time-integration schemes coupled with a diagonal mass matrix to reduce the time spent on solving the equation system. By employing a fictitious domain approach, this method also helps to eliminate some of the difficulties associated with mesh generation. Besides introducing a proper, specific mass lumping technique, we also study the performance of the low-order and high-order versions of this approach based on several numerical examples. Our results show that the high-order version of the spectral cell method together requires less memory storage and less CPU time than other possible versions, when combined simultaneously with explicit time-integration algorithms. Moreover, as the implementation of the proposed method in available finite element programs is straightforward, these properties turn the method into a viable tool for practical applications such as structural health monitoring 1–3], quantitative ultrasound applications 4], or the active control of vibrations and noise 5, 6]. |
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