Frequencies of circular plate with concentric ring and elastic edge support

doi:10.1007/s11465-014-0299-5

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 RAO^1,^*(

),Chellapilla Kameswara RAO^2,^*(

)

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

Download: PDF(218 KB) HTML
Export: BibTeX | EndNote | Reference Manager | ProCite | RefWorks

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 Author(s): 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:

https://academic.hep.com.cn/fme/EN/10.1007/s11465-014-0299-5
https://academic.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

Tab.1 The cross over radius, bcor and the corresponding frequency parameters, kcor for various values of R11 and T11=10

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

Tab.3 The cross over radius, bcor and the corresponding frequency parameters, kcor for various values of T11 and R11=10

Tab.4 Optimal locations (ring support, bopt & subsequent frequency, kopt) for R11=10 and different values of T11

Tab.5 Comparison of Fundamental frequency for ν=0.3, with Wang et al. [14] for free Edge

1	TimoshenkoS, Woinowsky-KriegerS. Theory of Plates and Shells. McGraw-Hill, New York, 1959
2	LeissaA W.Vibration of Plates. NASA SP-160, 1969
3	McleodA J, BishopR E D. The Forced Vibration of Circular Flat Plates. Mechanical Engineering Science Monograph, 1965, 1: 1–33
4	SzilardR. Theory and Analysis of Plates. Prentice-Hall, New Jersey, 1974
5	JawadM H. Design of plate and shell structures. ASME Three Park Avenue, New York, NY 10016, 2004
6	BodineR Y. The fundamental frequency of a thin, flat circular plate supported along a circle of arbitrary radius. Journal of Applied Mechanics, 1959, 26: 666–668
7	LauraP A A, GutierrezR H, VeraS A, VegaD A. Transverse vibrations of a circular plate with a free edge and a concentric circular support. Journal of Sound and Vibration, 1999, 223(5): 842–845 doi: 10.1006/jsvi.1998.2150
8	BodineR Y. Vibration of Circular Plate supported by a concentric ring of arbitrary radius. Journal of the Acoustical Society of America, 1967, 41(6): 1551 doi: 10.1121/1.1910524
9	KuklaS, SzewczykM. The Green’s functions for vibration problems of circular plates with elastic ring supports. Scientific Research of the Institute of Mathematics and Computer Science, 2004, 1(3): 67–72
10	MagrabE B.Vibrations of Elastic Structural Members. Sijthoff & Noordhoff. The Netherlands, 1979
11	WeisenselG N. Natural Frequency Information for Circular and Annular Plates. Journal of Sound and Vibration, 1989, 133(1): 129–134 doi: 10.1016/0022-460X(89)90987-5
12	AzimiS. Free Vibration of circular plates with elastic or rigid interior support. Journal of Sound and Vibration, 1988, 120(1): 37–52 doi: 10.1016/0022-460X(88)90333-1
13	WangC Y, WangC M. Fundamental Frequencies of Circular Plates with internal elastic ring support. Journal of Sound and Vibration, 2003, 263(5): 1071–1078 doi: 10.1016/S0022-460X(03)00275-X
14	WangC Y, WangC M. Buckling of Circular Plates with an internal ring support and elastically restrained edges. Thin-walled Structures, 2001, 39(9): 821–825 doi: 10.1016/S0263-8231(01)00031-3
15	KimC S, DickinsonS M. The Flexural Vibration of the Isotropic and Polar Orthotropic Annular and Circular Plates with elastically restrained peripheries. Journal of Sound and Vibration, 1990, 143(1): 171–179 doi: 10.1016/0022-460X(90)90576-L
16	RaoL B, RaoC K. Buckling of Annular Plates with Elastically Restrained External and Internal Edges. Mechanics Based Design of Structures and Machines: An International Journal, 2013, 41(2): 222–235 doi: 10.1080/15397734.2012.717495
17	WangC Y. On the fundamental frequency of a circular plate supported on a ring. Journal of Sound and Vibration, 2001, 243(5): 945–946 doi: 10.1006/jsvi.2000.3463

[1]	Bo WANG, Feng ZHAO, Zixu ZHAO, Kunpeng XU. Influence factors on natural frequencies of composite materials[J]. Front. Mech. Eng., 2020, 15(4): 571-584.
[2]	Ye GAO, Wei SUN. Inverse identification of the mechanical parameters of a pipeline hoop and analysis of the effect of preload[J]. Front. Mech. Eng., 2019, 14(3): 358-368.
[3]	Manman XU, Shuting WANG, Xianda XIE. Level set-based isogeometric topology optimization for maximizing fundamental eigenfrequency[J]. Front. Mech. Eng., 2019, 14(2): 222-234.
[4]	Jianghua FENG, Jing SHANG, Zhixue ZHANG, Huadong LIU, Zihao HUANG. Solid-state transformer-based new traction drive system and control[J]. Front. Mech. Eng., 2018, 13(3): 411-426.
[5]	Le YANG, Shuo WANG, Jianghua FENG. Electromagnetic interference modeling and suppression techniques in variable-frequency drive systems[J]. Front. Mech. Eng., 2018, 13(3): 329-353.
[6]	Shuaishuai WANG, Caichao ZHU, Chaosheng SONG, Huali HAN. Effects of elastic support on the dynamic behaviors of the wind turbine drive train[J]. Front. Mech. Eng., 2017, 12(3): 348-356.
[7]	F. H. ZHANG, S. F. WANG, C. H. AN, J. WANG, Q. XU. Full-band error control and crack-free surface fabrication techniques for ultra-precision fly cutting of large-aperture KDP crystals[J]. Front. Mech. Eng., 2017, 12(2): 193-202.
[8]	Mingjin XU,Yifan DAI,Xuhui XIE,Lin ZHOU,Shengyi LI,Wenqiang PENG. Ion beam figuring of continuous phase plates based on the frequency filtering process[J]. Front. Mech. Eng., 2017, 12(1): 110-115.
[9]	Pengxing YI,Peng HUANG,Tielin SHI. Numerical analysis and experimental investigation of modal properties for the gearbox in wind turbine[J]. Front. Mech. Eng., 2016, 11(4): 388-402.
[10]	M. R. AKBARI,D. D. GANJI,A. MAJIDIAN,A. R. AHMADI. Solving nonlinear differential equations of Vanderpol, Rayleigh and Duffing by AGM[J]. Front. Mech. Eng., 2014, 9(2): 177-190.
[11]	Qi XIA,Tao ZHOU,Michael Yu WANG,Tielin SHI. Shape and topology optimization for tailoring the ratio between two flexural eigenfrequencies of atomic force microscopy cantilever probe[J]. Front. Mech. Eng., 2014, 9(1): 50-57.
[12]	M.R. AKBARI,D.D. GANJI,A.R. AHMADI,Sayyid H. Hashemi KACHAPI. Analyzing the nonlinear vibrational wave differential equation for the simplified model of Tower Cranes by Algebraic Method[J]. Front. Mech. Eng., 2014, 9(1): 58-70.
[13]	Yancheng LI,Jianchun LI. Dynamic characteristics of a magnetorheological pin joint for civil structures[J]. Front. Mech. Eng., 2014, 9(1): 15-33.
[14]	Lokavarapu Bhaskara Rao, Chellapilla Kameswara Rao. Fundamental buckling of circular plates with elastically restrained edges and resting on concentric rigid ring support[J]. Front Mech Eng, 2013, 8(3): 291-297.
[15]	Lili CHEN, Wu ZHOU. Dependence of error sensitivity of frequency on bias voltage in force-balanced micro accelerometer[J]. Front Mech Eng, 2013, 8(2): 146-149.

Viewed

Full text

Abstract

Cited

Shared

Discussed