Vibrations of Circular Plates Resting on Elastic Foundation with Elastically Restrained Edge Against Translation

L.B. Rao, C.K. Rao

Abstract


The present paper deals with exact solutions for the free vibration characteristics of thin circular plates resting on Winkler-type elastic foundation based on the classical plate theory elastically restrained against translation. Parametric investigations are carried out for estimating the influence of edge restraint against translation and stiffness of the elastic foundation on the natural frequencies of circular plates. The elastic edge restraint against translation and the presence of elastic foundation has been found to have a profound influence on vibration characteristics of the circular plate undergoing free transverse vibrations. Computations are carried out for natural frequencies of vibrations for varying values of translational stiffness ratio and stiffness parameter of Winkler-type foundation. Results are presented for twelve modes of vibration both in tabular and graphical form for use in the design. Extensive data is tabulated so that pertinent conclusions can be arrived at on the influence of translational edge restraint and the foundation stiffness ratio of the Winkler foundation on the natural frequencies of uniform isotropic circular plates.  


Keywords


Plate; Frequency; Elastic edge; Translational stiffness; Elastic foundation.

Full Text:

PDF

References


Ascione L, Grimaldi A (1984), Unilateral contact between a plate and an elastic foundation. Mechanica 19(3): 223-233.

Bhaskara RL, Kameswara RC (2009), Buckling of circular plates with a ring support and elastically restrained edge. Advances in Vibration Engineering 8(1): 61-69.

Bhaskara RL, Kameswara RC (2010), Buckling analysis of circular plates with elastically restrained edges and resting on internal elastic ring support. Mechanics Based Design of Structures and Machines 38(4): 440-452.

Bhaskara RL, Kameswara RC (2015), Vibrations of a rotationally restrained circular plate resting on a concentric rigid ring support. International Journal of Acoustics and Vibration 20(4): 220-225.

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

Chang JY, Wickert JA (2001), Response of modulated doublet modes to traveling wave excitation. Journal of Sound and Vibration 242(1): 69-83.

Dempsey JP, Keer LM, Patel NB, Glasser ML (1984), Contact between plates and unilateral supports. Journal of Applied Mechanics 51(2): 324-328

Ghosh AK. (1997), Axisymmetric dynamic response of a circular plate on an elastic foundation. Journal of Sound and Vibration 205(1): 112-120.

Kang KH, Kim KJ (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.

Kim M, Moon J, Wickert JA (2000), Spatial modulation of repeated vibration modes in rotationally periodic structures. Journal of Vibration and Acoustics, Transactions of ASME 122(1): 62-68.

Kim KM, Kim MS (2001), Vibration of Beams with Generally Restrained Boundary Conditions using Fourier Series. Journal of Sound and Vibration 245(5): 771-784.

Leissa AW (1969), Vibration of plates (NASA SP-160). Office of Technology Utilization, Washington, DC.

Leissa AW (1993), Vibration of plates. Acoustical Society of America, Sewickley, PA.

Lokavarapu BRL, Chellapilla KR (2013), Fundamental buckling of circular plates with elastically restrained edges and resting on concentric rigid ring support. Frontiers of Mechanical Engineering 8(3): 291-297.

Lokavarapu BRL, Chellapilla KR (2015), Buckling of circular plate with foundation and elastic edge. International Journal of Mechanics and Materials in Design 11(2): 149-156.

Rao CK, Rao LB (2009), Vibrations of elastically restrained circular plates resting on partial Winkler foundation. The Open Acoustics Journal 2: 68-74.

Rao CK, Rao LB (2016), Vibrations of circular plate supported on a rigid concentric ring with translational restraint boundary. Engineering Transactions 64(3): 259-269.

Salari M, Bert CM, Striz AG (1987), Free vibration of a solid circular plate free at its edges and attached to a Winbkler foundation. Journal off Sound and Vibration 118(1): 188-191.

Soedel W (1993), Vibrations of shells and plates. Marcel Dekker, Inc., New York.

Tseng JG, Wickert JA (1994), On the vibration of bolted plate and flange assemblies. Journal of Vibration and Acoustics, Transactions of ASME 116(4): 468-473.

Wang JTS, Lin CC (1996), Dynamic analysis of generally supported beams using fourier series. Journal of Sound and Vibration 196(3): 285-293.

Wang CY, Wang CM (2003), Fundamental frequencies of circular plates with internal elastic ring support. Journal of Sound and Vibration 263: 1071-1078.

Wang CY (2005), Fundamental frequency of a circular plate supported by a partial elastic foundation. Journal of Sound and Vibration 285(4-5): 1203-1209.

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

Winkler E. (1867), Die Lehre von der Elasticitaet and Festigkeit, Prag. Dominicus.

Yayli MÖ, Aras M, Aksoy S (2014), An efficient analytical method for vibration analysis of a beam on elastic foundation with elastically restrained ends. Shock and Vibration 2014: 1-7.

Zheng XJ, Zhou YH (1988), Exact solution of nonlinear circular plate on elastic-foundation. Journal of Engineering Mechanics-ASCE 114: 1303-1316.




DOI: http://dx.doi.org/10.24200/tjer.vol15iss1pp14-25

Refbacks

  • There are currently no refbacks.




Copyright (c) 2018 L.B. Rao, C.K. Rao

Creative Commons License
This work is licensed under a Creative Commons Attribution-NoDerivatives 4.0 International License.

TJER 2017-CC BY-ND

This journal and its content is licensed under a Attribution-NoDerivatives 4.0 International.

Flag Counter