Free Vibrations of Thin‐Walled Bars with Open Cross Sections
Publication: Journal of Engineering Mechanics
Volume 113, Issue 10
Abstract
An application of the finite element method to the theory of thin‐walled bars of variable, open cross section is presented. A thin‐walled bar is considered as a special case of the membrane shell with internal constraints (Vlasov's and Wagner's assumptions). The bar is divided into elements along its longitudinal axis, then the shell midsurface of the element is approximated by arbitrary triangular subelements. Displacements of the element are represented by polynomials of the third degree, and both an equivalent stiffness matrix and a consistent mass matrix are obtained. An eigenvalue problem is analyzed using standard and generalized forms. Convergence of the method is discussed and numerical examples are presented for I‐beams of constant and variable cross sections.
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Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 113 • Issue 10 • October 1987
Pages: 1441 - 1453
Copyright
Copyright © 1987 ASCE.
History
Published online: Oct 1, 1987
Published in print: Oct 1987
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