Hostname: page-component-cd9895bd7-gbm5v Total loading time: 0 Render date: 2024-12-25T05:51:15.677Z Has data issue: false hasContentIssue false
  • English
  • Français

Dynamic Analysis of Circular Plate on Elastic Foundation by EFHT Method

Published online by Cambridge University Press:  05 May 2011

Lai-Yun Wu  and
Wen-Haur Lee
Lai-Yun Wu*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
Wen-Haur Lee*
Affiliation:
Department of Civil Engineering, National Taiwan University, Taipei, Taiwan 10617, R.O.C.
*
*Associate Professor
**Graduate student
Get access

Abstract

The dynamic response of a homogeneous, isotropic and elastic circular plate on an elastic foundation subjected to axisymmetric time dependent loads is investigated both analytically and numerically in thisv paper. First, the Extended Finite Hankel Transform (EFHT) is derived. After applying the technique of the EFHT to the governing equation of the vibrating circular plate, the governing partial differential equation (PDE) is transformed into the governing ordinary differential equation (ODE). Therefore, the analytical solution of the plate problem can be found completely. Once the dynamic response of the plate is solved, the internal forces of the plate, including shear force, bending moment and torsion, can be obtained subsequently. Under the particular case that elastic springs do not exist under the foundation, the dynamic response of the circular plate by the method of EFHT matches exactly with that by the method of modal analysis. By comparing the methods of EFHT, Boundary Element Method (BEM) and Finite Element Method (FEM), the results indicate that the proposed method of EFHT is accurate, systematic and convenient.

Keywords

Elastic foundationCircular plateDynamic responseExtended Finite Hankel TransformBoundary Element MethodFinite Element Method
Type
Articles
Information
Journal of Mechanics , Volume 19 , Issue 3 , September 2003 , pp. 337 - 347
Copyright
Copyright © The Society of Theoretical and Applied Mechanics, R.O.C. 2003

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

1.Flynn, P. D., “Elastic Response of Simple Structures to Pulse Loadings,” Ballistic Research Laboratories Memorandum Report No. 525, November (1950).Google Scholar
2.Kantham, C. L., “Bending and Vibration of Elastically Restrained Circular Plate,” Journal of the Franklin Institute, Vol. 265, 1958, pp. 483–491.CrossRefGoogle Scholar
3.Reismann, H., “Forced Vibrations of a Circular Plate,” Journal of Applied Mechanics, Vol. 26, Transaction ASME, Vol. 81, Series E, pp. 526–527 (1959).CrossRefGoogle Scholar
4.Weiner, R. S., “Forced Axisymmetric Motions of Circular Elastic Plates,” Journal of Applied Mechanics, Vol. 32, Transaction ASME, Vol. 87, Series E, pp. 893–898 (1965).CrossRefGoogle Scholar
5.Lee, T.-C., “An Extended Finite Hankel Transform and Its Application,” Journal of Applied Mechanics, Vol. 43, pp. 534–535, June (1974).CrossRefGoogle Scholar
6.Vivoli, J., and Filippi, P., “Eigenfrequencies of Thin Plates and Layer Potentials,” Journal of Acoustics Society of America, Vol. 55, pp. 562–567 (1974).CrossRefGoogle Scholar
7.Kitahara, M., “Boundary Integral Equation Methods in Eigenvalue Problems of Elasto-dynamics and Thin Plates,” Studies in Applied Mathematics, Elsevier, Amsterdam, p. 10 (1985).Google Scholar
8.Niwa, Y., Kobayashi, S. and Kitahara, M., “Eigenfrequency Analysis of a Plate by the Integral Equation Method,” Theoretical Applied Mathematics, University of Tokyo Press, Vol. 29, pp. 287–307 (1981).Google Scholar
9.Tranter, C. J., Integral Transforms in Mathematical Physics, John Wiley and Sons, Inc. (1951).Google Scholar
10.Zemanian, A. H., Generalized Integral Transformations, Dover Publications, Inc. (1987).Google Scholar