The compelled fluctuations of a rectangular two-layer piecewise-homogeneous plate of a constant thickness
( Pp. 25-30)

This article discusses forced vibrations of a rectangular two-layer piecewise homogeneous plate of constant thickness, when the material of the upper layer of the plate is elastic and the other satisfies Maxwell’s model, that is, viscoelastic. The transverse displacement of points of the contact plane of a two-layer plate is determined, which satisfies the approximate equation obtained in [1], replacing only the viscoelastic operators of the upper layer of the plate with the elastic Lames coefficients, respectively. Fluctuation rectangular is free a piecewise-homogeneous plate at nonzero initial conditions, frequencies of own fluctuations are calculated, and the analytical decision of this problem is under construction. 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 cross-section displacement of points of a plane of contact of plates at non-stationary external loadings.

Djalilov M.L., Rakhimov R.K., (2020), THE COMPELLED FLUCTUATIONS OF A RECTANGULAR TWO-LAYER PIECEWISE-HOMOGENEOUS PLATE OF A CONSTANT THICKNESS. Computational Nanotechnology, 4 => 25-30.

1. Rakhimov R.H., Umaraliev N., Dzhalilov M.L. Fluctuations of two-layer plates of a constant thickness. Computational Nanotechnology. 2018. No. 2. ISSN 2313-223X.
2. Ljav And. The mathematical theory of elasticity. Moscow - Leningrad: ONTI, 1935. 630 p.
3. Filippov I.G., Egorychev O.A. Wave processes in linear viscoelastic environments. Moscow: Mechanical Engineering, 1983. 272 p.
4. Chetaev N.G. Stability of movement. Moscow: Science, 1990. 176 p.
5. Achenbach J.D. An asymptotic method to analyze the vibrations of elastic layer. Trans. ASME. 1969. Vol. E 34. No. 1. Pp. 37-46.
6. Brunelle E.J. The elastics and dynamics of a transversely isotropic Timoshenko beam. J. Compos. Mater. 1970. Vol. 4. Pp. 404-416.
7. Gallahan W.R. On the flexural vibrations of circular and elliptical plates. Quart. Appl. Math. 1956. Vol. 13. No. 4. Pp. 371-380.
8. Dong S. Analysis of laminated shells of revolution. J. Esg. Mech. Div. Proc. Amer. Sac. Civil Engrs. 1966. Vol. 92. No. 6.
9. Jalilov M.L., Rakhimov R.Kh. Analysis of the general equations of the transverse vibration of a piecewise uniform viscoelastic plate. Computational Nanotechnology. 2020. Vol. 7. No. 3. Pp. 52-56. DOI: 10.33693/2313-223X-2020-7-3-52-56.

vibrations, two-layer plate, displacements, elastic, viscoelastic, boundary conditions, initial conditions, operator, Maxwell’s model, differential equation, hinged plastic, complex frequency, Poisson’s ratios, Fourier series, oscillation equations.