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Abstract

An analytical method is adopted to determine modal characteristics of non-linear spinning discs. The disc is assumed to be isotropic and rotating under steady-state conditions. The effects of amplitude and rotating speed on natural frequencies are determined. The developed procedure is also capable of analysing natural frequencies of linear free vibration, which is independent of amplitude. Attention is confined to determine natural frequencies, mode shapes, stress distributions, and critical speeds for different numbers of nodal diameters. The developed procedure does not consider modes of vibration corresponding to nodal circles. Validity of this procedure is verified by comparing some of the computed results with those established for certain cases.

Keywords

free transverse vibration non-linear vibration thin disc flexible rotating disc highspeed rotating disc critical speeds modal analysis

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References

Lamb

Southwell

R. V.

The vibrations of a spinning disk

Proc. R. Soc. Lond., 1922, 99, 272–280.

Southwell

R. V.

On the free transverse vibrations of a uniform circular disk clamped at its centre, and on the effects of rotation

Proc. R. Soc. Lond., 1922, 101, 133–153.

Parker

R. G.

Modeling and analysis of spinning disk-spindle vibration. In Proceedings of DETC97, ASME Design Engineering Technical Conferences, Sacramento, California, 1997, pp. 1–9.

Nowinski

J. L.

Nonlinear transverse vibrations of spinning disk

J. Appl. Mech., 1964, 31, 72–78.

Maher

J. F.

Adams

G. G.

Effect of displacement-dependent membrane stresses on the axisymmetric configuration of a spinning flexible disk

ATLE Tribol. Trans., 1991, 34 (4), 597–603.

Renshaw

A. A.

Mote

C. D.

A perturbation solution for the flexible rotating disk: Nonlinear equilibrium and stability under transverse loading

J. Sound Vibr., 1995, 183, 309–326.

Advani

S. H.

Bulkely

P. Z.

Nonlinear transverse vibrations and waves in spinning membrane disks

Int. J. Nonlinear Mech., 1969, 4, 123–127.

Malhotra

Namachchivaya

N. S.

Whalen

Finite amplitude dynamics of a flexible spinning disk. ASME Design Engineering Technical Conferences III, Part A, 1995, pp. 239–250.

Raman

Mote

C. D.

Nonlinear oscillations of circular plates near critical speed. Symposium on Nonlinear Dynamics and Stochastic Mechanics, IMECE, Dallas, Texas, 1997, DE-vol. 95, pp. 171–183.

10.

Boulabal

Crandall

S. H.

Self-excited harmonic and solitary waves in a spinning disk (with video presentation). ASME 16th Biennial Conference on Mechanical Vibration and Noise, Sacramento, California, 1997, DETC97/VIB-4093.

11.

Hamidzadeh

H. R.

Nepal

Dehghani

Transverse vibration of thin rotating disks - Nonlinear modal analysis. ASME International Mechanical Engineering Congress and Exposition, Anaheim, California, 1998, pp. 219–225, DE-98.

12.

Luo

A. C.J.

Mote

C. D.

An analytical solution of the non-linear vibration of rotating disks. ASME 17th Biennial Conference on Mechanical Vibration and Noise, Las Vegas, Nevada, 1999, DETC99/VIB-8150.

13.

Prescot

Applied elasticity, 1961 (Dover Publications, New York).

14.

Abramowitz

Stegun

I. A.

Handbook of mathematical functions with formulas, graphs, and mathematical tables, tenth printing, December 1972 (US Government Printing Office, Washington, DC).

Non-linear free transverse vibration of thin rotating discs

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