Free vibration analysis of elastic rods using global collocation |
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Authors: | Christopher G Provatidis |
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Institution: | (1) School of Mechanical Engineering, National Technical University of Athens, 9 Iroon Polytechniou Avenue, 157 73 Athens, Greece |
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Abstract: | This paper investigates the performance of a novel global collocation method for the eigenvalue analysis of freely vibrated
elastic structures when either basis or shape functions are used to approximate the displacement field. Although the methodology
is generally applicable, numerical results are presented only for rods in which one-dimensional basis functions in the form
of a power series, as well as equivalent Lagrange, Bernstein or Chebyshev polynomials are used. The new feature of the proposed
methodology is that it can deal with any type of boundary conditions; therefore, the cases of two Dirichlet as well as one
Dirichlet and one Neumann condition were successfully treated. The basic finding of this work is that all these polynomials
lead to results identical to those obtained by the power series expansion; therefore, the solution depends on the position
of the collocation points only. |
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Keywords: | Collocation Spectral methods Finite element Eigenvalue problem Elastodynamics |
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