American Society of Civil Engineers

Out-of-Plane Vibration of Thick Circular Ring

by James Kirkhope, (Assoc. Prof., Dept. of Mech. and Aeronautical Engrg., Carleton Univ., Ottawa, Canada)

Journal of the Engineering Mechanics Division
, Vol. 102, No. 2, March/April 1976, pp. 239-247

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Document type: Journal Paper
Abstract: Dynamic stiffness matrices are derived for the out-of-plane coupled twist-bending motion of a complete circular ring, and which take account of the effects of transverse shear and rotatory inertia. The accuracy of the matrices is assessed by comparison of calculated natural frequencies with experimental values obtained by other authors for thick rings having circular and rectangular cross sections. The simplest matrix, which leads to a quadratic frequency equation for the bending and torsion modes, is satisfactory only for modes involving two or three nodal diameters. The more complete matrix, which leads to a cubic frequency equation, is shown to accurately predict the bending and torsional frequencies of extremely thick rings vibrating in modes of up to ll nodal diameters.

ASCE Subject Headings:
Matrices (mathematics)