Mathematical Problems in Engineering
Volume 2007 (2007), Article ID 94035, 8 pages
Love and Rayleigh Correction Terms and Padé Approximants
1Institute of General Mechanics, Faculty of Mechanical Engineering, Rheinisch-Westfälische Technische Hochschule (RWTH), Aachen, Templergraben 64, Aachen 52056, Germany
2Department of Automatics and Biomechanics, Technical University of Łódź, Stefanowskiego 1/15, Łódź 90-924, Poland
Received 29 September 2006; Accepted 16 October 2006
Academic Editor: Semyon M. Meerkov
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.
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.