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Numerical study of the vibrations of an elastic container filled with an inviscid fluid
Author(s) -
Hermant Nicolas,
Chouly Franz,
Silva Fabrice,
Luizard Paul
Publication year - 2018
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201600208
Subject(s) - inviscid flow , added mass , container (type theory) , dimensionless quantity , vibration , fluid–structure interaction , finite element method , mechanics , parametric statistics , boundary value problem , normal mode , mass matrix , physics , matrix (chemical analysis) , mathematical analysis , classical mechanics , mathematics , materials science , thermodynamics , acoustics , statistics , composite material , nuclear physics , neutrino
We investigate numerically the vibrational behavior of an elastic structure containing an inviscid fluid with a filling hole where the pressure is prescribed. The underlying mathematical model is detailed and its spectra is characterized. The finite element method relies upon the added‐mass formulation of Morand and Ohayon but avoids the explicit assembly of the dense added‐mass matrix. A parametric study allows to characterize the system's response to dimensionless parameters in terms of eigenfrequencies. The resulting mode shapes are then physically discussed, with emphasis on the presence and the behavior of singular modes caused by specific boundary conditions in the fluid.