Vibration of shear deformable rings: Theory and experiment

• Published in: Journal of sound and vibration 1985-12, Vol.103 (4), p.549-565
• Main Authors: Gardner, T.G., Bert, C.W.
• Format: Article
• Language: English
• ISSN: 0022-460X; 1095-8568
• DOI: 10.1016/S0022-460X(85)80023-7

A new first-approximation theory is presented for analysis of the in-plane dynamic behavior of shear deformable ring structures. This theory may be applied to curved beams as well as complete rings. Natural frequencies and associated vibrational modes for a complete ring are investigated experimentally using modern instrumentation and experimental techniques. The natural frequencies predicted by the new theory are compared with the new experimental data as well as some previously reported data and predictions from thin-ring theory, various other shear deformable theories, elasticity theory, and various finite element analyses. The present theory includes a description of transverse shear strain which permits satisfaction of the physical requirements of zero shear stress at the inner-and outer-ring surfaces. Transverse shear strain is an important effect when analyzing thick, homogeneous, material rings and even more significant for rings made of composite materials. This theory is an advancement over Bresse-type, shear-correction theories, which utilize a shear correction factor determined in an ad hoc fashion.