Engineering Transactions, 64, 3, pp. 259-269, 2016
10.24423/engtrans.371.2016

### Vibrations of Circular Plate Supported on a Rigid Concentric Ring with Transnational Restraint Boundary

VIT University
India

Chellapilla Kameswara RAO
Nalla Narsimha Reddy Engineering College
India

This paper deals with frequency analysis of a circular plate supported on a rigid concentric ring with translational restrained boundary. Natural frequencies of such a circular plate are omputed for different sets of elastic translational restraints, and for various values of the radius of the internal ring support. Results for different modes of plate vibrations are computed and presented in a tabular form suitable for use in design. The effect of plate boundary conditions such as translational restraints and the radius of concentric ring support on natural frequencies of the circular plate are studied. Exact frequency values presented in this paper are expected to serve as benchmark solutions for assessing the accuracy of other numerical methods being used in the literature.
Keywords: circular plate; frequency; translational restraint; rigid ring; mode switching
Full Text: PDF

#### References

Leissa A.W., Vibrations of plates (NASA SP-160), Office of Technology Utilization, Washington, D.C., 1969.

Hughes T.J.R., The finite element method – linear static and dynamic finite element analysis, Prentice-Hall, Inc., Englewood Cliffs, NJ, 1987.

Katsikadelis J.T., The boundary element method for plate analysis, Elsevier, Amsterdam, 2014.

Katsikadelis J.T., A boundary element solution to the vibration problem of plates, Journal of Sound and Vibration, 141(2): 313–322, 1990.

Katsikadelis J.T., Sapountzakis E.J., Zorba E.G., A BEM approach to static and dynamic analysis with internal supports, Computational Mechanics, 7(1): 31–40, 1990.

Katsikadelis J.T., Kandilas C.B., A flexibility matrix solution of the vibration problem of plates based on the Boundary Element Method, Acta Mechanica, 83(1–2): 51–60, 1990.

Katsikadelis J.T., Sapountzakis E.J., A BEM solution to dynamic analysis of plates with variable thickness, Computational Mechanics, 7(5–6): 369–379, 1991.

Katsikadelis J.T., The analysis of plates on elastic foundation by the boundary element method, International Journal of Solids and Structures, 27(15): 1867–1878, 1991.

Gospodinov G., Liutskanov D., The boundary element applied to plates, Appl. Math. Modelling, 6: 237–244, August 1982.

Guminiak M., An alternative approach of initial stability analysis of Kirchhoff plates resting on internal supports by the Boundary Element Method, Engineering Transactions, 63(3): 273–296, 2015.

McLeod A.J., Bishop R.E.D., The forced vibration of circular flat plates, Mechanical Engineering Science Monograph 1, Institution of Mechanical Engineers, London, 1965.

Magrab E.B., Vibrations of elastic structural members, Mechanics of Structural Systems 3. Alphen aan den Rijn, Sijthoff & Noordhoff Intern. Publ. 1979.

Weisensel G.N., Natural frequency information for circular and annular Plates, Journal of Sound and Vibration, 133(1): 129–137, 1989.

Kim C.S., Dickinson S.M., The flexural vibration of the isotropic and polar orthotropic annular and circular plates with elastically restrained peripheries, Journal of Sound and Vibration, 143(1): 171–179, 1990.

Bhaskara Rao L., Kameswara Rao C., Vibrations of elastically restrained circular plates resting on Winkler foundation, Arabian Journal for Science and Engineering, 38(11): 3171–3180, 2013.

Rao L.B., Rao C.K., Vibrations of circular plates with guided edge and resting on elastic foundation, Journal of Solid Mechanics, 4(3): 307–312, 2012.

Azimi S., Free vibration of circular plates with elastic or rigid interior support, Journal of Sound and Vibration, 120(1): 37–52, 1988.

Ding Z., Free vibration of arbitrary shaped plates with concentric ring elastic and/or rigid supports, Computers19. Wang C.Y., On the fundamental frequency of a circular plate supported on a ring, Journal of Sound and Vibration, 243(5): 945–946, 2001.

Wang C.Y., On the fundamental frequency of a circular plate supported on a ring, Journal

of Sound and Vibration, 243(5): 945–946, 2001.

Wang C.Y., Wang C.M., Buckling of circular plates with an internal ring support and elastically restrained edges, Thin-Walled Structures, 39(9): 821–825, 2001.

Rao L.B., Rao C.K., Buckling analysis of circular plates with elastically restrained edges and resting on internal elastic ring support, Mechanics Based Design of Structures and Machines: An International Journal, 38(4): 440–452, 2010.

Bodine R.Y., The fundamental frequencies of a thin, flat circular plate simply supported along a circle of arbitrary radius, ASME, Paper no. APMW-10, Journal of Applied Mechanics, 26: 666–668, 1959.

Laura P.A.A., Gutierrez R.H., Cortinez V.H., Utjes J.C., Transverse vibrations of a circular plates and membranes with intermediate supports, Journal of Sound and Vibration, 113(1): 81–86, 1987.

Bodine R.Y., Vibration of circular plate supported by a concentric ring of arbitrary radius, Journal of the Acoustical Society of America, 41(6): 1551, 1967.

DOI: 10.24423/engtrans.371.2016