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Frontiers of Mechanical Engineering

Front. Mech. Eng.    2014, Vol. 9 Issue (2) : 168-176     https://doi.org/10.1007/s11465-014-0299-5
RESEARCH ARTICLE |
Frequencies of circular plate with concentric ring and elastic edge support
Lokavarapu Bhaskara RAO1,*(),Chellapilla Kameswara RAO2,*()
1. SMBS, VIT University, Chennai Campus, Vandalur-Kelambakkam Road, Chennai-600127, Tamil Nadu, India
2. Department of Mechanical Engineering, Guru Nanak Institutions Technical Campus, Ibrahimpatnam, Hyderabad - 501506, A.P, India
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Abstract

Exact solutions for the flexural vibrations of circular plates having elastic edge conditions along with rigid concentric ring support have been presented in this paper. Values of frequency parameter for the considered circular plate are computed for different sets of values of elastic rotational and translation restraints and the radius of internal rigid ring support. The results for the first three modes of plate vibrations are computed and are presented in tabular form. The effects of rotational and linear restraints and the radius of the rigid ring support on the vibration behavior of circular plates are studied over a wide range of non-dimensional parametric values. The values of the exact frequency parameter presented in this paper for varying values of restraint parameters and the radius of the rigid ring support can better serve in design and as benchmark solutions to validate the numerical methods obtained by using other methods of solution.

Keywords circular plate      frequency      elastic edge      rigid ring      mode switching     
Corresponding Authors: Lokavarapu Bhaskara RAO   
Issue Date: 22 May 2014
 Cite this article:   
Lokavarapu Bhaskara RAO,Chellapilla Kameswara RAO. Frequencies of circular plate with concentric ring and elastic edge support[J]. Front. Mech. Eng., 2014, 9(2): 168-176.
 URL:  
http://journal.hep.com.cn/fme/EN/10.1007/s11465-014-0299-5
http://journal.hep.com.cn/fme/EN/Y2014/V9/I2/168
Fig.1  Concentric rigid ring supported circular plate with elastically restrained boundary
Fig.2  Fundamental frequency of circular plate and concentric rigid support radius for R11=2.5&T11=10
Fig.3  Frequency of circular plate and concentric rigid support radius for R11=5&T11=10
Fig.4  Fundamental frequency of circular plate and concentric rigid support radius for R11=20&T11=10
Fig.5  Fundamental frequency of circular plate and concentric rigid support radius for R11=50&T11=10
Fig.6  Fundamental frequency of circular plate and concentric rigid support radius for R11=100&T11=10
Fig.7  Fundamental frequency of circular plate and concentric rigid support radius for R11=500&T11=10
Fig.8  Fundamental frequency of circular plate and concentric rigid support radius for R11=1000&T11=10
Fig.9  Fundamental frequency of circular plate and concentric rigid support radius for R11=1010&T11=10
R112.55205010050010001016
bcor0.099850.095300.089110.087010.086790.086140.086010.08597
kcor2.750332.754772.762.760502.761632.762462.762732.76272
Tab.1  The cross over radius, bcor and the corresponding frequency parameters, kcor for various values of R11 and T11=10
R112.55205010050010001016
bopt0.60.60.60.60.60.60.60.6
kopt3.632983.726013.856063.894053..908083.919723.921213.9227
Tab.2  Optimal locations (concentric ring support, bopt & subsequent frequency parameter, kopt for various values of R11 and T11=10
Fig.10  Fundamental frequency of circular plate and concentric rigid support radius for T11=2.5&R11=10
Fig.11  Fundamental frequency of circular plate and concentric rigid support radius for T11=5&R11=10
Fig.12  Fundamental frequency of circular plate and concentric rigid support radius for T11=20&R11=10
Fig.13  Fundamental frequency of circular plate and concentric rigid support radius for T11=50&R11=10
Fig.14  Fundamental frequency of circular plate and concentric rigid support radius for T11=100&R11=10
Fig.15  Fundamental frequency of circular plate and concentric rigid support radius for T11=500&R11=10
Fig.16  Fundamental frequency of circular plate and concentric rigid support radius for T11=1000&R11=10
Fig.17  Fundamental frequency of circular plate and concentric rigid support radius for T11=1016&R11=10
T112.55205010050010001016
bcor0.098370.096400.082820.063780.046020.021840.019240.016
kcor2.415732.548333.052683.543053.909904.361304.424064.48074
Tab.3  The cross over radius, bcor and the corresponding frequency parameters, kcor for various values of T11 and R11=10
T112.55205010050010001016
bopt0.60.60.60.50.50.40.40.4
kopt3.679983.723793.936654.261434.70335.759275.933864.48074
Tab.4  Optimal locations (ring support, bopt & subsequent frequency, kopt) for R11=10 and different values of T11
Ring support radius, bWang et al. [14])Present
000
0.021.5011.50077
0.051.6341.63422
0.11.7891.78911
0.151.9221.92226
0.22.0512.05103
Tab.5  Comparison of Fundamental frequency for ν=0.3, with Wang et al. [14] for free Edge
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