Re-investigation of large-amplitude free vibrations of beams using finite elements

An iterative procedure is developed to solve the dynamic finite-element equations for the large-amplitude free vibration of a uniform elastic beam. Harmonic oscillations are assumed; the equations corresponding to the axial and out-of-plane directions are satisfied exactly; and the converged mode sh...

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Bibliographic Details
Published in:Journal of sound and vibration 1990-12, Vol.143 (2), p.351-355
Main Authors: Singh, G., Venkateswara Rao, G., Iyengar, N.G.R.
Format: Article
Language:English
Subjects:
Exact sciences and technology
Fundamental areas of phenomenology (including applications)
Physics
Solid mechanics
Structural and continuum mechanics
Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...)
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Summary:An iterative procedure is developed to solve the dynamic finite-element equations for the large-amplitude free vibration of a uniform elastic beam. Harmonic oscillations are assumed; the equations corresponding to the axial and out-of-plane directions are satisfied exactly; and the converged mode shape is used to reduce the matrix equations to a scalar equation which is solved by the direct numerical integration method of Woinowsky- Krieger (1950). Numerical results for beams with immovable edges and hinged-hinged, fixed-hinged, and fixed-fixed boundary conditions are presented in tables and briefly characterized. It is shown that neglecting the axial displacements in the calculation leads to significant overprediciton of the nonlinear frequencies. For an amplitude ratio equal to unity, the rise in frequency due to geometrical nonlinearity is about 1.33 times higher with the harmonic-oscillations assumption than without it. (T.K.)
ISSN:0022-460X
1095-8568
DOI:10.1016/0022-460X(90)90958-3