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Keywords: DSC-Ritz element method, rectangular Mindlin plates, mixed edge supports.

Summary

This paper applies a newly developed discrete singular convolution (DSC)-Ritz element method to investigate the free vibration of rectangular plates having edge support discontinuities. The Mindlin shear deformable plate theory [1] is employed in this study. The Ritz trial functions for the displacements of the plates are established through the DSC delta type wavelet kernel [2]. The nodal displacements at plate edges are incorporated into the Ritz trial functions which are employed to enforce the geometric boundary conditions of the plates with mixed edge support conditions.

Three square Mindlin plates with different mixed edge constraints are selected to examine the validity and accuracy of the proposed numerical method. Convergence studies are carried out for the selected plates against the number of DSC grid points used in the calculation. It is found that in general the frequency parameters of the plate decrease as the DSC grid point size increases. Small oscillations of the frequency parameters are evident while the DSC grid point size increases. The frequency parameters calculated using the current DSC-Ritz method with the DSC grid point size greater than 30 is in close agreement with those by Liu and Liew [3] who employed the differential quadrature element method in their study.

New frequency parameters are presented for a rectangular Mindlin plate with mixed free, simply supported and clamped edge conditions. As expected, increasing the clamped portion on an edge with mixed support conditions leads to the increase of the frequency parameters. The frequency parameters of a thicker plate are lower than its thinner counterpart.

The paper demonstrates the capability and flexibility of the DSC-Ritz element method for the analysis of rectangular Mindlin plates with mixed edge supports. The method can be easily extended to analyse plates of arbitrary shapes with edge support discontinuities, which the conventional Ritz method has difficulties to treat. Future work on the vibration analyses of skew plates and triangular plates having edge support discontinuities will be reported.

References

1: R.D. Mindlin, "Influence of rotary inertia and shear in flexural motion of isotropic, elastic plates", Journal of Applied Mechanics-ASME, 18, 31-38, 1951.
2: G.W. Wei, Y.B. Zhao, Y. Xiang, "Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm", International Journal for Numerical Methods in Engineering, 55, 913-946, 2002. doi:10.1002/nme.526
3: F.L. Liu, K.M. Liew, "Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method", Journal of Sound and Vibration, 225, 915-934, 1999. doi:10.1006/jsvi.1999.2262

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Front Page Browse CCP CSETS CTR IJRT Other Authors Search Purchase Guide FAQ Contact us	Civil-Comp Proceedings ISSN 1759-3433 CCP: 91 PROCEEDINGS OF THE TWELFTH INTERNATIONAL CONFERENCE ON CIVIL, STRUCTURAL AND ENVIRONMENTAL ENGINEERING COMPUTING Edited by: B.H.V. Topping, L.F. Costa Neves and R.C. Barros Paper 188 Vibration Analysis of Rectangular Mindlin Plates with Mixed Edge Supports Y. Xiang¹, S.K. Lai², L. Zhou¹ and C.W. Lim³ ¹School of Engineering, University of Western Sydney, Penrith South DC, NSW, Australia ²Division of Building Science and Technology, ³Department of Building and Construction, City University of Hong Kong, Kowloon, Hong Kong, PR China doi:10.4203/ccp.91.188 purchase the full-text of this paper Full Bibliographic Reference for this paper Y. Xiang, S.K. Lai, L. Zhou, C.W. Lim, "Vibration Analysis of Rectangular Mindlin Plates with Mixed Edge Supports", in B.H.V. Topping, L.F. Costa Neves, R.C. Barros, (Editors), "Proceedings of the Twelfth International Conference on Civil, Structural and Environmental Engineering Computing", Civil-Comp Press, Stirlingshire, UK, Paper 188, 2009. doi:10.4203/ccp.91.188 Keywords: DSC-Ritz element method, rectangular Mindlin plates, mixed edge supports. Summary This paper applies a newly developed discrete singular convolution (DSC)-Ritz element method to investigate the free vibration of rectangular plates having edge support discontinuities. The Mindlin shear deformable plate theory [1] is employed in this study. The Ritz trial functions for the displacements of the plates are established through the DSC delta type wavelet kernel [2]. The nodal displacements at plate edges are incorporated into the Ritz trial functions which are employed to enforce the geometric boundary conditions of the plates with mixed edge support conditions. Three square Mindlin plates with different mixed edge constraints are selected to examine the validity and accuracy of the proposed numerical method. Convergence studies are carried out for the selected plates against the number of DSC grid points used in the calculation. It is found that in general the frequency parameters of the plate decrease as the DSC grid point size increases. Small oscillations of the frequency parameters are evident while the DSC grid point size increases. The frequency parameters calculated using the current DSC-Ritz method with the DSC grid point size greater than 30 is in close agreement with those by Liu and Liew [3] who employed the differential quadrature element method in their study. New frequency parameters are presented for a rectangular Mindlin plate with mixed free, simply supported and clamped edge conditions. As expected, increasing the clamped portion on an edge with mixed support conditions leads to the increase of the frequency parameters. The frequency parameters of a thicker plate are lower than its thinner counterpart. The paper demonstrates the capability and flexibility of the DSC-Ritz element method for the analysis of rectangular Mindlin plates with mixed edge supports. The method can be easily extended to analyse plates of arbitrary shapes with edge support discontinuities, which the conventional Ritz method has difficulties to treat. Future work on the vibration analyses of skew plates and triangular plates having edge support discontinuities will be reported. References 1 R.D. Mindlin, "Influence of rotary inertia and shear in flexural motion of isotropic, elastic plates", Journal of Applied Mechanics-ASME, 18, 31-38, 1951. 2 G.W. Wei, Y.B. Zhao, Y. Xiang, "Discrete singular convolution and its application to the analysis of plates with internal supports. Part 1: Theory and algorithm", International Journal for Numerical Methods in Engineering, 55, 913-946, 2002. doi:10.1002/nme.526 3 F.L. Liu, K.M. Liew, "Analysis of vibrating thick rectangular plates with mixed boundary constraints using differential quadrature element method", Journal of Sound and Vibration, 225, 915-934, 1999. doi:10.1006/jsvi.1999.2262 purchase the full-text of this paper (price £20) go to the previous paper go to the next paper return to the table of contents return to the book description purchase this book (price £140 +P&P)
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