Summary
The effects of higher-order deformations on natural frequencies and buckling stresses of a thick circular ring with rectangular cross-sections subjected to circumferential tensile and/or compressive stresses are studied. Based on the power series expansion of displacement components, a set of fundamental dynamic equations of a one-dimensional higher-order ring theory is derived through Hamilton's sprinciple. Several sets of truncated approximate theories which can take into account the complete effects of higher-order deformations such as shear deformation and depth change and rotary inertia are applied to solve the eigenvalue problems of a thick circular ring. In order to assure the accuracy of the present theory, convergence properties of the minimum natural frequency and the buckling stress for the flexural and extensional displacement modes of thick rings are examined in detail. It seems that the present approximate theories can predict benchmark data of the natural frequency and buckling stress of thick rings more accurately compared to other existing theories.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Kuhl, W.: Messungen zu den Theorien der Eigenschwingungen von Kreisringen beliebiger Wandstärke. Akust. Z.7, 125–152 (1942).
Seidel, B. S., Erdelyi, E. A.: On the vibration of a thick ring in its own plane. J. Eng. Indust.86 B, 240–244 (1964).
Kirkhope, J.: Simple frequency expression of in-plane vibrations of annular rings. J. Acoust. Soc. Am.59, 86–89 (1976).
Kirkhope, J.: In-plane vibration of a thick circular ring. J. Sound Vibr.50, 219–227 (1977).
Gardner, T. G., Bert, C. W.: Vibration of shear deformable rings: theory and experiment. J. Sound Vibr.103, 549–565 (1985).
Bhimaraddi, A.: Generalized analysis of shear deformable rings and curved beams. Int. J. Solids Struct.24, 363–373 (1988).
Matsunaga, H.: In-plane vibration and stability of shallow circular arches subjected to axial forces. Int. J. Solids Struct.33, 469–482 (1996).
Yokoo, Y., Matsunaga, H.: A general nonlinear theory of elastic shells. Int. J. Solids Struct.10, 261–274 (1974).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Matsunaga, H. Effects of higher-order deformations on in-plane vibration and stability of thick circular rings. Acta Mechanica 124, 47–61 (1997). https://doi.org/10.1007/BF01213017
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01213017