International audienceIn this paper, an efficient and robust numerical method is proposed to solve non-symmetric eigenvalue problems resulting from the spatial discretization with the finite element method of a vibroacoustic interior problem. The proposed method relies on a perturbation method. Finding the eigenvalues consists in determining zero values of a scalar that depends on angular frequency. Numerical tests show that the proposed method is not sensitive to poorly conditioned matrices resulting from the displacement-pressure formulation. Moreover, the computational times required with this method are lower than those needed with a classical technique such as, for example, the Arnoldi method. (C) 2016 Academie des sciences. Published by Elsevier Masson SAS. This is an open access article under the CC BY-NC-ND license
This paper concerns the study of vibroacoustic problems. By considering a displacement-pressure formulation, a non-symmetric eigenvalue problem is obtained. In order to solve it, three numerical schemes are compared: the classical ARPACK solver, an indicator method (initially proposed in B. Claude et al. Comptes Rendus Mécaniques, 2017, 345(2)) which has the property to be null at the eigenvalues, and an original method based on the analysis of Taylor series expansions near a singularity. Numerical results show all the evaluated numerical methods give accurate results but the indicator method requires the lowest computational times. Nevertheless, the original method based on the behavior of the perturbation method close to eigenvalues seems to be a very promising technique.
This paper concerns numerical simulations of time-dependent problems in computational solid mechanics. A perturbation method, with the time as perturbation parameter, is proposed to solve two classical problems: an elastic bar excited by an end force and the dynamic buckling of a cylindrical panel. Specific quadratic recast of the equations is proposed to solve the nonlinear problems. Numerical results show that asymptotic time expansions is robust, efficient and gives more accurate solutions than the ones obtained with classical time-integration schemes (implicit or explicit), even when the considered meshes are coarse.
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