Analysis of the general equations of the transverse vibration of a piecewise uniform viscoelastic plate
( Pp. 52-56)

More about authors
Rakhimov Rustam Kh. Dr. Sci. (Eng.), Professor; Head at the Laboratory No. 1
Institute of Materials Science of the SPA “Physics-Sun” of the Academy of Science of Uzbekistan
Tashkent, Republic of Uzbekistan Djalilov Mamatisa L. Cand. Sci. (Eng.); Head at the Department “Computer Systems”
Fergana branch of the Tashkent University of Information Technologies named after Muhammad Al-Khorazmiy
Fergana, Republic of Uzbekistan
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Abstract:
This article discusses the analysis of the general equations of the transverse vibration of a piecewise homogeneous viscoelastic plate obtained in the “Oscillation of inlayer plates of constant thickness” [1]. In the present work on the basis of a mathematical method, the approached theory of fluctuation of the two-layer plates, based on plate consideration as three dimensional body, on exact statement of a three dimensional mathematical regional problem of fluctuation is stood at the external efforts causing cross-section fluctuations. The general equations of fluctuations of piecewise homogeneous viscoelastic plates of the constant thickness, described in work [1], are difficult on structure and contain derivatives of any order on coordinates x, y and time t and consequently are not suitable for the decision of applied problems and carrying out of engineering calculations. For the decision of applied problems instead of the general equations it is expedient to use confidants who include this or that final order on derivatives. The classical equations of cross-section fluctuation of a plate contain derivatives not above 4th order, and for piecewise homogeneous or two-layer plates the elementary approached equation of fluctuation is the equation of the sixth order. On the basis of the analytical decision of a problem the general and approached decisions of a problem are under construction, are deduced the equation of fluctuation of piecewise homogeneous two-layer plates taking into account rigid contact on border between layers, and also taking into account mechanical and rheological properties of a material of a plate. The received theoretical results for the decision of dynamic problems of cross-section fluctuation of piecewise homogeneous two-layer plates of a constant thickness taking into account viscous properties of their material allow to count more precisely the is intense-deformed status of plates at non-stationary external loadings.
How to Cite:
Rakhimov R.K., Djalilov M.L., (2020), ANALYSIS OF THE GENERAL EQUATIONS OF THE TRANSVERSE VIBRATION OF A PIECEWISE UNIFORM VISCOELASTIC PLATE. Computational Nanotechnology, 3 => 52-56. DOI: 10.33693/2313-223X-2020-7-3-52-56
Reference list:
Rakhimov R.Kh., Umaraliev N., Djalilov M.L. Oscillations of bilayer plates of constant thickness. Computational Nanotechnology. 2018. No. 2. ISSN 2313-223X.
Love A. Mathematical theory of elasticity. Moscow-Leningrad: ONTI, 1935. 630 p.
Filippov I.G., Egorychev O.A. Wave processes in linear viscoelastic media. Moscow: Mechanical Engineering, 1983. 272 p.
Achenbach J.D. An asymptotic method to analyze the vibrations of elastic layer. Trans. ASME. 1969. Vol. E 34. No. 1. Pp. 37-46.
Brunelle E.J. The elastics and dynamics of a transversely isotropic Timoshenko beam. J. Compos. Mater. 1970. Vol. 4. Pp. 404-416.
Brunelle E.J. Buckling of transversely isotropic Mindlen plates. AIAA. 1971. Vol. 9. No. 6. Pp. 1018-1022.
Callahan W.R. On the flexural vibrations of circular and elliptical plates. Quart. Appl. Math. 1956. Vol. 13. No. 4. Pp. 371-380.
Dong S. Analysis of laminated shells of revolution. J. Esg. Mech. Div. Proc. Amer. Sac. Civil Engrs. 1966. Vol. 92. No. 6.
Dong S., Pister R.S., Taylor R.L. On the theory of laminated anisotropic shells and plates. J. of the Aerosp. Sci. 1962. Vol. 29. No. 8.
Keywords:
analysis, approximate, vibrations, two-layer plate, boundary value problem, stresses, deformation, oscillation equations.


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