Transverse Vibration of Clamped and Simply Supported Circular Plates with an Eccentric Circular Perforation and Attached Concentrated Mass

Subject Areas : Engineering

S.M  Mirkhalaf Valashani ¹ (Department of Mechanical Engineering, Islamic Azad University, Arak Branch)

Received: 2009-02-25 Accepted : 2009-04-25 Published : 2009-04-30

Keywords: Vibration, Circular plate, Eccentric circular perforation, Concentrated mass,

Abstract :

In this investigation Rayleigh-Ritz variational method has been applied to determine the least natural frequency coefficient for the title problem. Classical plate theory assumptions have been used to calculate strain energy and kinetic energy. Coordinate functions are combination of polynomials which satisfy boundary conditions at the outer boundary and trigonometric terms. In the second part of this study ABAQUS software is used to compute vibration natural frequency for some special combinations of geometrical and mechanical parameters. Then results of Rayleigh-Ritz method have been obtained for the mentioned special cases. It can be seen that the agreement between them is acceptable.

References:

[1] Jacquot R.G., Lindsay J.E., 1977, On the influence of Poisson’s ratio on circular plates natural frequencies, Journal of Sound and Vibration 52: 603-605.

[2] Laura P.A.A., Grossi R.O., 1978, Influence of Poisson’s ratio on the lower natural frequencies of transverse vibration of a circular plate of linearly varying thickness and with an edge elastically restrained against rotation, Journal of Sound and Vibration 60(4): 587-590.

[3] Gutierrez R.H., Laura P.A.A., 1977, A note on the determination of the fundamental frequency of vibration of rectangular and circular plates supporting masses distributed over a finite area, Applied Acoustics 10: 303-313.

[4] Narita Y., Leissa A.W., 1980, Transverse vibration of simply supported circular plates having partial elastic constraints, Journal of Sound and Vibration 70(1): 103-116.

[5] Laura P.A.A., Paloto J.C., Santos R.D., 1975, A note on the vibration and stability of a circular plate elastically restrained against rotation, Journal of Sound and Vibration 41(2): 177-180.

[6] Laura P.A.A., Luisoni L.E., Lopez J.J., 1976, A note on free and forced vibrations of circular plates: the effect of support flexibility, Journal of Sound and Vibration 47(2): 287-291.

[7] Irie T., Yamada G., Tanaka K., 1983, Free vibration of circular plate elastically restrained along some radial segments, Journal of Sound and Vibration 89(3): 295-308.

[8] Grossi R.O., Laura P.A.A., 1987, Additional results of transverse vibrations of polar orthotropic circular plates carrying concentrated masses, Applied Acoustics 21: 225-233.

[9] Laura P.A.A., Gutierrez R.H., 1991, Free vibration of solid circular plate of linearly varying thickness and attached to a winkler foundation, Journal of Sound and Vibration 144(1): 149-161.

[10] Bercin A.N., 1996, Free vibration solution for clamped orthotropic plates using the Kantorovich method, Journal of Sound and Vibration 196(2): 243-247.

[11] Ranjan V., Gosh M.K., 2006, Transverse vibration of thin solid and annular circular plate with attached discrete masses, Journal of Sound and Vibration 292: 999-1003.

[12] Kang W., Lee N.-H., Pang Sh., Chung W.Y., 2005, Approximate closed form solutions for free vibration of polar orthotropic circular plates, Applied Acoustics 66: 1162-1179.

[13] Park Ch., 2008, Frequency equation for the in-plane vibration of a clamped circular plate, Journal of Sound and Vibration 313: 325-333.

[14] Avalos D.R., Larrondo H.A., Laura P.A.A., Sonzogni V., 1998, Transverse vibrations of circular plate with a concentric square hole with free edges, Journal of Sound and Vibration 209(5): 889-891.

[15] Bambill D.V., La Malfa S., Rossit C.A., Laura P.A.A., 2004, Analytical and experimental investigation on transverse vibrations of solid, circular and annular plates carrying a concentrated mass at an arbitrary position with marine applications, Ocean Engineering 31: 127-138.

[16] Laura P.A.A., Masia U., Avalos D.R., 2006, Small amplitude transverse vibrations of circular plates elastically restrained against rotation with an eccentric circular perforation with a free edge, Journal of Sound and Vibration 292: 1004-1010.