Convergence of eigenvalues of a cantilever beam with 8- and 20-node hexahedral elements

Rajendran, S and Prathap, Gangan (1999) Convergence of eigenvalues of a cantilever beam with 8- and 20-node hexahedral elements. Journal of Sound and vibration, 227 (3). pp. 667-681.

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    Abstract

    The finite element discretization of a vibration problem replaces the original structure by a mass matrix, M, and a stiffness matrix K. The accuracy of the solution depends on the quality of both the stiffness and mass matrices. Clear guidelines exist as to how K is to be derived using an energy (or variational or virtual work) principle. Early attempts to deal with dynamics took the simplistic13; course of quot;quot;lumpingquot; quot; the mass of the element at the element nodes. The lumped mass matrix is diagonal and hence does not involve mass coupling between the degrees of13; freedom. It was realized [1, 2] that, from Hamilton's principle, a non-diagonal or quot;quot;consistentquot; quot; mass matrix could be derived from the kinetic energy by using the same trial functions that were used to determine the stiffness matrix. In a variational sense therefore, the quot;quot;lumpedquot; quot; mass approaches are quot;quot;non-consistentquot;quot;; they conserve mass but not necessarily momentum or kinetic energy of the 13; consistent mass matrix.

    Item Type: Journal Article
    Additional Information: Copyright for this article belongs to Elsevier Science
    Uncontrolled Keywords: Convergence of eigenvalues;Cantilever beam;Hexahedral;13; Discretization;Hamilton principle
    Subjects: ENGINEERING > Fluid Mechanics and Thermodynamics
    PHYSICS > Physics(General)
    Division/Department: Structures Division, Structures Division
    Depositing User: Mr. N A
    Date Deposited: 11 Aug 2008
    Last Modified: 03 May 2012 11:41
    URI: http://nal-ir.nal.res.in/id/eprint/1444

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