Abstract
The hyperbolic system of equations that describes the vibrations of plates inhomogeneous along one rectangular coordinate in the context of the Timoshenko theory is presented in canonical hamiltonian form, assuming the solution is periodic on a second coordinate. In the case of periodic inhomogeneity we study the structure of the solutions of certain wave boundary-value problems for plates of this type using the general properties of periodic hamiltonian systems. Bibliography: 6 titles.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Literature Cited
E. I. Grigolyuk and I. T. Selezov, eds.,Mechanics of Solid Deformable Bodies [in Russian], Vol. 1, Nonclassical Theories of the Vibrations of Rods, Plates, and Shells, Moscow (1993).
N. A. Kil'chevskii,A Course of Theoretical Mechanics [in Russian], Vol. 2, Moscow (1977).
V. V. Bolotin,Dynamic Stability of Elastic systems [in Russian], Moscow (1956).
L. Brillouin and M. Parodi,Propagation of Waves in Periodic Structures [Russian translation], Moscow (1959).
N. A. Shul'ga,Foundations of the Mechanics of Stratified Media of Periodic Structure [in Russian], Kiev (1981).
V. A. Yakubovich and E. M. Starzhinskii,Linear Differential Equations with Periodic Coefficients and their Applications [in Russian], Moscow (1972).
Additional information
Translated fromTeoreticheskaya i Prikladnaya Mekhanika, No. 26, 1996, pp. 105–111.
Rights and permissions
About this article
Cite this article
Shul'ga, O.M. Wave solutions of equations of Timoshenko type for the transverse vibrations of plates with parameters periodic on one coordinate. J Math Sci 86, 3153–3156 (1997). https://doi.org/10.1007/BF02355716
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02355716