Assignment of Geometrical and Physical Parameters for the Confinement of Vibrations in Flexible Structures
Publication: Journal of Aerospace Engineering
Volume 22, Issue 4
Abstract
A strategy for confinement of flexural vibrations in flexible structures by proper selection of their geometrical and physical parameters is proposed. We first show that the problem of vibration confinement can be formulated as an inverse eigenvalue problem (IEP) where the mode shapes and/or natural frequencies are assumed and the geometrical and physical properties are unknown functions of the space variables. It is required that the assumed modes form a complete and independent set of spatial functions that satisfy the boundary conditions and guarantee confinement within the desired spatial subdomain(s) of the structure. Using simple spatial functions, such as polynomials and exponentials, we determined approximate solutions of the geometrical and physical parameters by applying the orthogonality of the mode shapes with respect to the stiffness and mass density. The order of the selected polynomials or exponentials depends on the number of modes retained in the discretized model. Numerical simulations are presented on a beam and then on a plate to examine convergence of the solution to the IEP. We show that convergence is attained with few assumed mode shapes. The approximated parameters are finally substituted into the forward eigenvalue problem to confirm confinement at the desired locations.
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Published In
Journal of Aerospace Engineering
Volume 22 • Issue 4 • October 2009
Pages: 403 - 414
Copyright
© 2009 ASCE.
History
Received: Mar 12, 2008
Accepted: Sep 23, 2008
Published online: Sep 15, 2009
Published in print: Oct 2009
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