Vibrations of Circular Plates with Guided Edge and Resting on Elastic Foundation

Document Type: Research Paper


1 School of Mechanical and Building Sciences, VIT University, Chennai Campus, Vandalur-Kelambakkam Road

2 Department of Mechanical Engineering, Gurnanak Institutions and Technical Campus, Ibrahimpatnam


In this paper, transverse vibrations of thin circular plates with guided edge and resting on Winkler foundation have been studied on the basis of Classical Plate Theory. Parametric investigations on the vibration of circular plates resting on elastic foundation have been carried out with respect to various foundation stiffness parameters. Twelve vibration modes are presented. The location of the stepped region with respect to foundation stiffness parameter is presented.


[1] Timoshenko S., Krieger S.W., 1959, Theory of Plates and Shells, McGraw-Hill Book Company Inc, Newyork, Chapter 8:265.

[2] Leissa A.W., 1969, Vibration of Plates (NASA SP-160), Office of Technology Utilization, Washington, DC.

[3] Szilard R., 2004, Theories and Applications of Plate Analysis, Classical Numerical and Engineering Methods, John Wiley & Sons Inc, Chapter 3.

[4] Chakraverty S., 2009, Vibration of Plates, CRC Press, Taylor & Francis Group , Chapter 4.

[5] Wang C.Y., Wang C.M., 2003, Fundamental frequencies of circular plates with internal elastic ring support, Journal of Sound and Vibration 263: 1071-1078.

[6] Leissa A. W., 1993, Vibration of Plates, Acoustical Society of America, Sewickley, PA.

[7] Salari M., Bert C. M., Striz A.G., 1987, Free Vibration of a Solid Circular Plate free at its edge and attached to a Winkler foundation, Journal of Sound and Vibration 118: 188-191.

[8] Ascione L., Grimaldi A., 1984, Unilateral contact between a plate and an elastic foundation, Mechanica 19: 23-233.

[9] Kang K.H., Kim K.J., 1996, Modal properties of beams and plates on resilient supports with rotational and translational complex stiffness, Journal of Sound and Vibration 190(2): 207-220.

[10] Zheng X. J., Zhou Y. H., 1988, Exact solution of nonlinear circular plate on elastic-foundation, Journal of Engineering Mechanics-ASCE 114: 1303-1316.

[11] Ghosh A. K., 1997, Axisymmetric dynamic response of a circular plate on an elastic foundation, Journal of Sound and Vibration 205: 112-120.

[12] Winkler E., 1867, Die Lehre von der Elasticitaet and Festigkeit, Prag, Dominicus.

[13] Soedel W., 1993, Vibrations of shells and plates, Mareel Dekker, Inc.

[14] Weisman Y., 1970, On foundations that react in compression only, Journal of Applied Mechanics 37: 1019-1030.

[15] Dempsey J. P., Keer L. M., Patel N. B., Glasser M. L.,1984, Contact between plates and unilateral supports, Journal of Applied Mechanics 51: 324-328.

[16] Celep Z., 1988, Circular plate on tensionless Winkler foundation, Journal of Engineering Mechanics 114(10): 1723-1739.