Love and Rayleigh Correction Terms and Padé Approximants

Andrianov, I.; Awrejcewicz, J.

doi:https://doi.org/10.1155/2007/94035

Mathematical Problems in Engineering

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Research Article | Open Access

Volume 2007 | Article ID 094035 | https://doi.org/10.1155/2007/94035

Love and Rayleigh Correction Terms and Padé Approximants

I. Andrianov¹and J. Awrejcewicz²

Academic Editor: Semyon M. Meerkov

Received29 Sept 2006

Accepted16 Oct 2006

Published26 Dec 2006

Abstract

Simplified theories governing behavior of beams and plates keeping the fundamental characteristics of the being modeled objects are proposed and discussed. By simplification, we mean decrease of order of partial differential equations (PDEs) with respect to spatial coordinates. Our approach is used for both discrete and continuous models. An advantage of Padé approximation is addressed. First part of this report deals with approximation of a beam equation by string-like one, and plate equation by membrane-like one. Second part is devoted to the construction of Love-type theory for rods vibrations and Rayleigh-type theory for beams vibrations.

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Copyright

Copyright © 2007 I. Andrianov and J. Awrejcewicz. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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