Love and Rayleigh correction terms and Padé approximants
Summary: We propose and discuss simplified theories governing the behavior of beams and plates and keeping the fundamental characteristics of the objects. By simplification, we mean decrease of order of partial differential equations with respect to spatial coordinates. Our approach is used for both discrete and continuous models. An advantage of Padé approximation is addressed. The first part of this report deals with approximation of beam equation by string-like one, and plate equation by membrane-like one. The second part is devoted to the construction of Love-type theory for rod vibrations and Rayleigh-type theory for beam vibrations.
scientific article; zbMATH DE number 5311256