Setting the Linear Oscillations of Structural Heterogeneity Viscoelastic Lamellar Systems with Point Relations
ABSTRACT
The paper solves the problem of the variation formulation of the steady-linear oscillations of structurally inhomogeneous viscoelastic plate system with point connections. Under the influence of surface forces, range of motion and effort varies harmonically. The problem is reduced to solving a system of algebraic equations with complex parameters. The system of inhomogeneous linear equations is solved by the Gauss method with the release of the main elements in columns and rows of the matrix. For some specific problems, the amplitude-frequency characteristics are obtained.
The paper solves the problem of the variation formulation of the steady-linear oscillations of structurally inhomogeneous viscoelastic plate system with point connections. Under the influence of surface forces, range of motion and effort varies harmonically. The problem is reduced to solving a system of algebraic equations with complex parameters. The system of inhomogeneous linear equations is solved by the Gauss method with the release of the main elements in columns and rows of the matrix. For some specific problems, the amplitude-frequency characteristics are obtained.
Cite this paper
Safarov, I. , Akhmedov, M. and Boltaev, Z. (2015) Setting the Linear Oscillations of Structural Heterogeneity Viscoelastic Lamellar Systems with Point Relations. Applied Mathematics, 6, 228-234. doi: 10.4236/am.2015.62022.
Safarov, I. , Akhmedov, M. and Boltaev, Z. (2015) Setting the Linear Oscillations of Structural Heterogeneity Viscoelastic Lamellar Systems with Point Relations. Applied Mathematics, 6, 228-234. doi: 10.4236/am.2015.62022.
References
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[1] Safarov, I.I., Teshaev, M.K.H. and Madjidov, M. (2014) Damping Dissipation—Inhomogeneous Mechanical Systems. Lambert Academic Publishing (LAP), Germany, 217 p. [2] Chen, Y. (1963) On the Vibrations of Beams or Rods Carrying a Concentrated Mass. Journal of Applied Mechanics, 30, 310-311. [3] Bazarov, M.B., Safarov, I.I. and Shokin, Y.M. (1996) Numerical Simulation Fluctuations Dissipative Heterogeneous and Homogeneous Mechanical Systems. Siberian Branch, Novosibirsk, 189 p. [4] Safarov, I.I. (1992) Oscillations and Waves in Dissipative Inhomogeneous Media and Designs. Publishing “Science”, Tashkent. [5] Timoshenko, S.P. and Voynovskiy, S. (1966) Krieger Plates and Shells. McGran Hill Book Company, Inc., New York, Toronto, London, 636 p. [6] Sachenkov, A.V. and Hemp, Y.G. (1975) Vibrations of Rectangular Plates on Point Support. Applied Mehanika. Kiev, T.XI, 37-41. [7] Sunchaliev, R.M. and Filatov, A.N. (1972) On Some Methods for the Study of Nonlinear Problems in the Theory of Viscoelasticity. Journal of Academy of Sciences Reports, Moscow, 206, 201-203. [8] Jilin, P.A. (2006) Fundamentals of the Theory of Shells. Publishing House of the Polytechnic, University Press, St. Petersburg, 167 p.