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Projection and variational approaches to spectral analysis of thick elastic beams
Author(s) -
Kostin Georgy
Publication year - 2017
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201710132
Subject(s) - isotropy , section (typography) , projection (relational algebra) , mathematical analysis , projection method , beam (structure) , symmetry (geometry) , vibration , cross section (physics) , mathematics , ode , homogeneous , physics , geometry , computer science , optics , statistical physics , algorithm , quantum mechanics , grating , operating system
Variational and projectional approaches based on the method of integro‐differential relations is applied to derive finite‐dimensional systems of ODEs approximating the natural vibrations of rectilinear elastic beams with the rectangular cross‐section. This technique involves special semi‐discrete integral projections of constitutive equations relating the stress and strain tensors as well as the velocity and momentum vectors. The spectral properties of a homogeneous isotropic beam with the square cross section are analyzed by taking into account the problem symmetry. (© 2017 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)