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 Pade 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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Institute of General Mechanics, Faculty of Mechanical Engineering, Rheinisch-Westfalische Technische Hochschule (RWTH), Aachen, Templergraben 64, 52056 Aachen, Germany;
