AM  Vol.5 No.19 , November 2014
Natural Oscillations of Viscoelastic Lamellar Mechanical Systems with Point Communications
ABSTRACT
We investigated the natural oscillations of dissipative inhomogeneous plate mechanical systems with point connections. Based on the principle of virtual displacements, we equate to zero the sum of all active work force, including the force of inertia which obtain equations vibrations of mechanical systems. Frequency equation is solved numerically by the method of Muller. According to the result of numerical analysis we established nonmonotonic dependence damping coefficients of the system parameters.

Cite this paper
Ibrahimovich, S. , Hudoyberdievich, T. and Maqsud, M. (2014) Natural Oscillations of Viscoelastic Lamellar Mechanical Systems with Point Communications. Applied Mathematics, 5, 3018-3025. doi: 10.4236/am.2014.519289.
References
[1]   Andreyev, L.V., Dyshko, A.L. and Pavlenko, I.D. (1988) Dinamika of Plates and Covers with the Concentrated. Mashinostroyeniye, Nauka, Moscow, 200p.

[2]   Gershgorin, S.A. (1933) Fluctuations of the Plates Loaded by Concentrated Mass. PMM, T.1, Volume 1, No. 1, 25-37.

[3]   Andreyev, L.V., Dyshko, A.L. and Pavlenko, I.D. (1980) Otsenki of the Main Frequency of Fluctuations of Plates and the Covers Bearing the Concentrated Weight. Izv.Vuzov. Aircraft Equipment, No. 2, 89-93.

[4]   Zhigalko, Yu.P. and Dmitriyev, L.I. (1978) Dinamika of Ridge Plates and Covers. Research on the Theory of Plates and Covers. Kazan, Issue 132, 3-30.

[5]   Majboroda, V.P., Troyanovskiy, I.E. and Safarov, I.I. (1983) Free and Forced Vibrations of Systems of Rigid Bodies in the Inhomogeneous Viscoelastic Dampers. Izv.AN USSR. Ser. “Engineering” No. 3.

[6]   Bozorov, M.B., Safarov, I.I. and Shokin, Yu.I. (1966) Numerical Modeling of Fluctuations of Dissipatively Uniform and Non-Uniform Mechanical Systems. Siberian Branch of the Russian Academy of Science, Novosibirsk, 188p.

[7]   Safarov, I.I., Teshayev, M.H. and Madjidov, M.A. (2014) Damping of Fluctuations Dissipatively—Non-Uniform Mechanical Systems. LAP LAMBERT Academic Publishing, Germany, 97p.

[8]   Kravchuk, A.S., Mayboroda, V.P. and Urzhumayev, Yu.S. (1985) Mekhanika of Polymeric and Composite Materials: Experimental and Numerical Methods. Nauka, Moscow, 304p.

[9]   Koltunov, M.A. (1976) Polzuchest and Relaxation. M.: The Highest Scale, 277p.

[10]   Safarov, I.I. (1992) Waves in Inhomogeneous Media and Dissipative Structures. Nauka, Tashkent, 250p.

[11]   Safarov, I.I. (1985) Damping Structurally Inhomogeneous System with a Finite Number of Degrees of Freedom. Differential Equations and Their Applications to Mechanics, Nauka, Tashkent, 288-294.

 
 
Top