Abstract
In this paper, the modified iteration method is successfully extended to investigate the nonlinear free vibration of corrugated circular plates with full corrugations. The analytical relation for the amplitude-frequency response of corrugated circular plates is obtained and discussions on the influences of geometrical parameters on vibration behaviours of corrugated circular plates are made. The present results are practically important in the design of elastic elements in precision instruments.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Liu, R. H., The characteristic relations of corrugated circular plates,Acta Mechanica Sinica,1 (1978), 47. (in Chinese)
Liu, R. H., The characteristic relations of corrugated circular plates with plane central regions,Journal of China University of Science and Technology.9, 2 (1979), 75. (in Chinese)
Liu, R. H., Large deflection of corrugated circular plate with a plane central region under the action of concentrated loads at the center.International Journal of Non-Linear Mechanics,19, 5 (1984). 409.
Liu, R. H., Large deflection of corrugated circular plate with plane boundary region,Solid Mechanics Archives,9, 4 (1984), 383.
Liu, R. H., Nonlinear bending of corrugated annular plates,Scientia Sinica, series A,27, 6 (1984), 640.
Liu, R. H., Nonlinear analysis of corrugated annular plates under compound load,Scientia Sinca, series A,28, 9 (1985), 959.
Liu, R. H., On large deflection of corrugated annular plates under uniform presssure,The Advances of Applied Mathematics and Mechanics in China,1 (1987), 138.
Liu, R. H., The study on nonlinear bending problems of corrugated circular plates, The International Conference of Humboldt Foundation, Shanghai, (1987).
Liu, R. H., Nonlinear analysis of a corrugated circular plate under combined lateral loading,Applied Mathematics and Mechanics,9, 8 (1988), 711–726
Andryewa, L. E., The calculation of a corrugated membrane as an anisotropic plate,The Engineer's Collection.21 (1955). 128. (in Russian)
Yeh, K. Y., Liu, R. H. et al., Nonlinear stability of thin circular shallow spherical shell under actions of axisymmetric uniformly distributed line loads.Journal of Lanzhou University,2 (1965), 10;Bulletin of Sciences.2 (1965), 142. (in Chinese)
Yeh, K. Y., Liu, R. H. et al., Nonlinear stability of thin circular shallow spherical shell under the action of uniform edge moment.Bulletin of Sciences,2 (1965). 145. (in Chinese)
Liu, R. H., Nonlinear stability of circular shallow spherical shell with a hole in the center under the action of uniform moment at the inner edge.Bulletin of Sciences,3 (1965), 253. (in Chinese)
Liu, R. H., and Li, D., On the nonlinear bending and vibration of corrugated circular plates,International Journal of Non-Linear Mechanics,24 (1989). (in press)
Wang, X. Z. et al., Nonlinear vibration of circular corrugated plates.Applied Mathematics and Mechanics,8, 3 (1987), 241–250.
Huang, C. L. and B. E. Sandman, Large amplitude vibrations of rigidly clamped circular plates.International Journal of Non-Linear Mechanics,6 (1971), 451.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Dong, L., Ren-huai, L. Application of the modified iteration method to nonlinear vibration of corrugated circular plates. Appl Math Mech 11, 13–22 (1990). https://doi.org/10.1007/BF02014567
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02014567