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Civil-Comp Proceedings
ISSN 1759-3433 CCP: 79
PROCEEDINGS OF THE SEVENTH INTERNATIONAL CONFERENCE ON COMPUTATIONAL STRUCTURES TECHNOLOGY Edited by: B.H.V. Topping and C.A. Mota Soares
Paper 258
Non-Linear Free Vibrations of Rectangular Plates: u-v-w Formulation K. El Bikri+, R. Benamar* and M.M.K. Bennouna#
+Laboratory of Applied Mechanics and Technology, High School for Technology Education, Rabat, Morocco
Full Bibliographic Reference for this paper
K. El Bikri, R. Benamar, M.M.K. Bennoun, "Non-Linear Free Vibrations of Rectangular Plates: u-v-w Formulation", in B.H.V. Topping, C.A. Mota Soares, (Editors), "Proceedings of the Seventh International Conference on Computational Structures Technology", Civil-Comp Press, Stirlingshire, UK, Paper 258, 2004. doi:10.4203/ccp.79.258
Keywords: geometrically non-linear vibration, coupled transverse-in-plane displacements, rectangular plate.
Summary
In a previous series of papers [1,2], the geometrically non-linear free vibrations
of isotropic thin rectangular plates with fully clamped edges, undergoing large
amplitude flexural deflections, have been studied using Hamilton's principle and
spectral analysis. In the previous formulation, called in what follows the "
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The objective of this paper is to generalize and extend the model for non-linear
free vibrations of a fully clamped thin isotropic rectangular plate developed
previously in [1] in order to examine qualitatively and quantitatively the coupling
between the transverse and the membrane displacements in the non-linear range.
Three coupled sets of non-linear algebraic equations have been obtained, which
reduces, once the in-plane inertia is neglected, to one set of non-linear algebraic
equations in term of the contribution coefficient of the transverse displacement only.
This set, which is similar to that obtained in [1,2,3], involves a new general term of
the fourth non-linear rigidity tensor
Judicious choice of admissible and compatible basic functions for a fully
clamped-immovable rectangular plate has been made and both iterative and explicit
analytical method have been employed to solve the amplitude equations of motion in
order to establish the validity of the present
Hence, accurate estimates of the fundamental non-linear natural frequency have
been obtained for a wide range of vibration amplitudes. The fundamental amplitude
dependent non-linear mode including both axial displacement References
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