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Derivation of New Transcendental Member Stiffness Determinant for Vibrating Frames

Author(s):

Medium: journal article
Language(s): English
Published in: International Journal of Structural Stability and Dynamics, , n. 2, v. 3
Page(s): 299-305
DOI: 10.1142/s0219455403000835
Abstract:

Transcendental dynamic member stiffness matrices for vibration problems arise from solving the governing differential equations to avoid the conventional finite element method (FEM) discretization errors. Assembling them into the overall dynamic structural stiffness matrix gives a transcendental eigenproblem, whose eigenvalues (natural frequencies or their squares) are found with certainty using the Wittrick–Williams algorithm. This paper gives equations for the recently discovered transcendental member stiffness determinant, which equals the appropriately normalized FEM dynamic stiffness matrix determinant of a clamped ended member modelled by infinitely many elements. Multiplying the overall transcendental stiffness matrix determinant by the member stiffness determinants removes its poles to improve curve following eigensolution methods. The present paper gives the first ever derivation of the Bernoulli–Euler member stiffness determinant, which was previously found by trial-and-error and then verified. The derivation uses the total equivalence of the transcendental formulation and an infinite order FEM formulation, which incidentally gives insights into conventional FEM results.

Structurae cannot make the full text of this publication available at this time. The full text can be accessed through the publisher via the DOI: 10.1142/s0219455403000835.
  • About this
    data sheet
  • Reference-ID
    10353297
  • Published on:
    14/08/2019
  • Last updated on:
    14/08/2019
 
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