Nonlinear vibrations of a viscoelastic plate with concentrated masses |
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Authors: | D A Khodzhaev B Kh Éshmatov |
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Institution: | (1) Tashkent Institute Irrigation and Melioration, Tashkent, 700000, Uzbekistan;(2) Polytechnic Institute and State University of Virginia, Blacksburg, 24061, USA |
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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 δ-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.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 6, pp. 158–169, November–December, 2007. |
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Keywords: | viscoelastic plate concentrated mass nonlinear vibrations Bubnov-Galerkin method relaxation kernel |
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