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Prikladnaya Mekhanika i Tekhnicheskaya Fizika, 2007, Volume 48, Issue 6, Pages 158–169
(Mi pmtf2103)
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This article is cited in 8 scientific papers (total in 8 papers)
Nonlinear vibrations of a viscoelastic plate with concentrated masses
D. A. Khodzhaeva, B. Kh. Eshmatovb a Tashkent Institute Irrigation and Melioration, Tashkent, 700000, Uzbekistan
b Polytechnic Institute and State University of Virginia, Blacksburg, 24061, USA
Abstract:
The problem of vibrations of a viscoelastic plate with concentrated masses is studied in a geometrically nonlinear formulation. In the equation of motion of the plate, the action of the concentrated masses is taken into account using Dirac $\delta$-functions. The problem is reduced to solving a system of Volterra type ordinary nonlinear integrodifferential equations using the Bubnov–Galerkin method. The resulting system with a singular Koltunov–Rzhanitsyn kernel is solved using a numerical method based on quadrature formulas. The effect of the viscoelastic properties of the plate material and the location and amount of concentrated masses on the vibration amplitude and frequency characteristics is studied. A comparison is made of numerical calculation results obtained using various theories.
Keywords:
viscoelastic plate, concentrated mass, nonlinear vibrations, Bubnov–Galerkin method, relaxation kernel.
Received: 23.01.2006 Accepted: 22.11.2006
Citation:
D. A. Khodzhaev, B. Kh. Eshmatov, “Nonlinear vibrations of a viscoelastic plate with concentrated masses”, Prikl. Mekh. Tekh. Fiz., 48:6 (2007), 158–169; J. Appl. Mech. Tech. Phys., 48:6 (2007), 905–914
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https://www.mathnet.ru/eng/pmtf2103 https://www.mathnet.ru/eng/pmtf/v48/i6/p158
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