Frequency Aanalysis of Annular Plates Having a Small Core and Guided Edges at Both Inner and Outer Boundaries

Document Type : Research Paper


1 School of Mechanical and Building Sciences, VIT University, Chennai Campus, Vandalur-Kelambakkam Road, Chennai-600127, Tamil Nadu, India

2 Nalla Narsimha Reddy Engineering College, Korremula 'X' Road, Chowdariguda (V), Ghatkesar (M), Ranga Reddy (dt) - 500088, Telangana State, India


This paper deals with frequency analysis of annular plates having a small core and guided edges at both inner and outer boundaries. Using classical plate theory the governing differential equation of motion for the annular plate having a small core is derived and solved for the case of plate being guided at inner and outer edge boundaries. The fundamental frequencies for the first six modes of annular plate vibrations are computed for different materials and varying values of the radius parameter. The fundamental frequencies thus obtained may be classified into to axisymmetric and/or non-axisymmetric modes of vibration. The exact values of fundamental frequencies presented in this paper clearly show that no mode switching takes place for the case of annular plates with guided edges. The results presented in this paper will be of use in design and also serve as benchmark values to enable the researchers to validate their results obtained using numerical methods such as differential quadrature or finite element methods.


[1] Leissa A.W., 1969, Vibration of Plates, NASA SP-160.
[2] Leissa A.W., 1977, Recent research in plate vibrations: classical theory, Shock and Vibration Digest 9(10): 13-24.
[3] Leissa A.W., 1987, Recent research in plate vibrations, classical theory, Shock and Vibration Digest 19: 11-18.
[4] Weisensel G.N., 1989, Natural frequency information for circular and annular plates, Journal of Sound and Vibration 133(1): 129-134.
[5] Soedel W., 1993, Vibrations of Shells and Plates, Marcel Dekker, New York.
[6] Gabrielson T.B., 1999, Frequency constants for transverse vibration of annular disks, Journal of the Acoustical Society of America 105(6): 3311-3317.
[7] Irie T., Yamada G., Takagi K., 1982, Natural frequencies of thick annular plates, Journal of Applied Mechanics 49(3): 633-638.
[8] Ramaiah G. K., 1980, Flexural vibrations of annular plates under uniform in-plane compressive forces, Journal of Sound and Vibration 70(1): 117-131.
[9] Vera S.A., Laura P.A.A., Vega D.A., 1999, Transverse vibrations of a free-free circular annular plate, Journal of Sound and Vibration 224(2): 379-383.
[10] Amabili M., Garziera R., 1999, Comments and additions to transverse vibrations of circular, annular plates with several combinations of boundary conditions, Journal of Sound and Vibration 228: 443-447.
[11] Southwell R.V., 1922, On the transverse vibrations of uniform circular disc clamped at its center and the effects of rotation, Proceedings of the Royal Society of London A 101(709): 133-153.
[12] Kim C.S., Dickinson S.M., 1990, The flexural vibration of thin isotropic and polar orthotropic annular and circular plates with elastically restrained peripheries, Journal of Sound and Vibration 143(1): 171-179.
[13] Bhaskara Rao L., Kameswara Rao C., 2011, Fundamental buckling of annular plates with elastically restrained guided edges against translation, Mechanics Based Design of Structures and Machines 39(4): 409-419.
[14] Bhaskara Rao L., Kameswara Rao C., 2012, Vibrations of circular plates with guided edge and resting on elastic foundation, Journal of Solid Mechanic 4(3): 307-312.
[15] Wang C.Y., Wang C.M., 2005, Examination of the fundamental frequencies of annular plates with small core, Journal of Sound and Vibration 280(3-5): 1116-1124.