Abstract
A technique for analyzing the natural vibrations of variable-thickness plates under in-plane loading has been developed. The technique is based on variational and R-function methods. It is used to study the dependence of the natural frequencies of the plates on their shape and boundary and loading conditions
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
REFERENCES
Ya. M. Grigorenko and A. M. Timonin, “An approach to the numerical solution of two-dimensional problems of plate and shell theory with variable parameters,” Int. Appl. Mech., 23, No.6, 557–563 (1987).
G. Z. Gevorkyan, “Free transverse vibrations of rectangular orthotropic variable-thickness plates with transverse shears taken into account,” in: Abstracts of Papers Read at the 8th All-Russian Congr. on Theoretical and Applied Mechanics [in Russian], Izd. UrO RAN, Ekaterinburg (2001), p. 177.
L. V. Kurpa and A. B. Linnik, “Solving stability and vibration problems for in-plane loaded plates of complex geometry,” Probl. Mashinostr., 2, No.1–2, 93–102 (1999).
V. L. Rvachev and L. V. Kurpa, R-functions in Problems of the Theory of Plates [in Russian], Naukova Dumka, Kiev (1987).
S. P. Timoshenko, A Course of the Theory of Elasticity [in Russian], Naukova Dumka, Kiev (1972).
S. Yu. Fialko, “Natural vibrations of complex bodies,” Int. Appl. Mech., 40, No.1, 83–90 (2004).
Ya. M. Grigorenko and A. T. Vasilenko, “Some approaches to the solution of problems on thin shells with variable geometrical and mechanical parameters,” Int. Appl. Mech., 38, No.11, 1309–1341 (2002).
P. A. A. Laura, H. A. Larrondo, V. H. Cortinez, and D. R. Avalos, “Transverse vibrations of rectangular plates of non-uniform thickness subjected to a uniform state of in-plane stress,” J. Sound Vibrat., 151(1), 175–180 (1991).
V. F. Meish and N. V. Kravchenko, “Nonaxisymmetric vibrations of discretely reinforced inhomogeneous multilayer cylindrical shells under nonstationary loads,” Int. Appl. Mech., 39, No.9, 1066–1072 (2003).
E. I. Starovoitov, D. V. Leonenko, and A. V. Yarovaya, “Vibrations of circular sandwich plates under resonance loads,” Int. Appl. Mech., 39, No.12, 1458–1463 (2003).
T. Y. Wu and G. R. Liu, “Free vibration analysis of circular plates with variable thickness by the generalized differential quadrature rule,” Int. J. Solids Struct., 38, No.44–45, 7967–7980 (2001).
Author information
Authors and Affiliations
Additional information
__________
Translated from Prikladnaya Mekhanika, Vol. 41, No. 1, pp. 85–93, January 2005.
Rights and permissions
About this article
Cite this article
Kurpa, L.V., Linnik, A.B. Studying the Vibrations of In-plane Loaded Plates of Variable Thickness. Int Appl Mech 41, 62–69 (2005). https://doi.org/10.1007/s10778-005-0059-7
Received:
Issue Date:
DOI: https://doi.org/10.1007/s10778-005-0059-7