Numerical determination of the density profile of an inhomogeneous membrane: solution of the inverse vibration problem

Autor:	Charles F Osborne, Steven Homolya, Imants D. Svalbe
Rok vydání:	2003
Předmět:	Surface (mathematics) Acoustics and Ultrasonics business.industry Mechanical Engineering Mathematical analysis Holography Inverse Inverse problem Condensed Matter Physics law.invention Vibration Optics Membrane Mechanics of Materials law Molecular vibration Vibration Problem business Mathematics
Zdroj:	Journal of Sound and Vibration. 261:193-211
ISSN:	0022-460X
DOI:	10.1016/s0022-460x(02)01072-6
Popis:	Given one or more vibrational modes of a membrane, the free vibration equation can be applied to infer the mass surface density. This paper considers determining the surface density of an inhomogeneous membrane from digitized holographic projections (interferograms) of the modeshapes. Spatially discrete numerical models of the membrane surface are presented, which can be used to solve both forward and inverse vibration problems. The accuracy of the discrete models is examined for exactly solvable free vibration problems involving inhomogeneous membranes. For the solution of the inverse problem, error estimates are given for the mass surface density deduced from modeshape interferograms. The practicability of the method is investigated using simulated experimental data for membranes with composite and continuously inhomogeneous density profiles. Strategies are discussed for reducing errors in the reconstructed densities.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::e1d60b1713e664e7ebc59efeab25f191 https://doi.org/10.1016/s0022-460x(02)01072-6 Zobrazit plný text záznamu Full Text from ScienceDirect