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Condensation of independent variables in free vibration analysis of curved beams
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 Title & Authors
Condensation of independent variables in free vibration analysis of curved beams
Mochida, Yusuke; Ilanko, Sinniah;
 Abstract
In this paper, the condensation method which is based on the Rayleigh-Ritz method, is described for the free vibration analysis of axially loaded slightly curved beams subject to partial axial restraints. If the longitudinal inertia is neglected, some of the Rayleigh-Ritz minimization equations are independent of the frequency. These equations can be used to formulate a relationship between the weighting coefficients associated with the lateral and longitudinal displacements, which leads to "connection coefficient matrix". Once this matrix is formed, it is then substituted into the remaining Rayleigh-Ritz equations to obtain an eigenvalue equation with a reduced matrix size. This method has been applied to simply supported and partially clamped beams with three different shapes of imperfection. The results indicate that for small imperfections resembling the fundamental vibration mode, the sum of the square of the fundamental natural and a non-dimensional axial load ratio normalized with respect to the fundamental critical load is approximately proportional to the square of the central displacement.
 Keywords
condensation method;connection coefficient matrix;slightly curved beam;natural frequencies;axial load;
 Language
English
 Cited by
1.
Isogeometric method based in-plane and out-of-plane free vibration analysis for Timoshenko curved beams,;;;

Structural Engineering and Mechanics, 2016. vol.59. 3, pp.503-526 crossref(new window)
1.
Isogeometric method based in-plane and out-of-plane free vibration analysis for Timoshenko curved beams, Structural Engineering and Mechanics, 2016, 59, 3, 503  crossref(new windwow)
 References
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2.
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3.
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4.
Ilanko, S. and Dickinson, S.M. (1987), "Linearization of the strain energy expressions for a vibrating slightly curved beam subjected to an axial load", J. Sound Vib., 108, 357-359.

5.
Ilanko, S. and Dickinson, S.M. (1987), "The vibration and post-buckling of geometrically imperfect, simply supported, rectangular plates under uni-axial loading, Part I: theoretical approach", J. Sound Vib., 118(2), 313-336. crossref(new window)

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