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Non‐Linear Vibration of a Cantilever Beam of Variable Cross‐Section
Author(s) -
Pielorz A.,
Nadolski W.
Publication year - 1986
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19860660304
Subject(s) - cantilever , beam (structure) , galerkin method , cross section (physics) , vibration , ordinary differential equation , mathematical analysis , constant (computer programming) , variable (mathematics) , mathematics , section (typography) , amplitude , differential equation , physics , nonlinear system , structural engineering , optics , acoustics , engineering , computer science , quantum mechanics , programming language , operating system
Large amplitude free vibration of an inextensible thin elastic beam of a variable cross‐section is analysed. Although large deflections and rotations are considered the strains are small. It is shown how approximate solutions can be obtained by using Galerkin's method, and the effect of the variation of cross‐section is investigated. For the beam of constant cross‐section the results are compared with those of paper [3] and the exact solution of the special case of an ordinary differential equation obtained in the paper is considered. Additionally, a simple method for static deflections of the beam is proposed.