Free vibrations of a viscoelastic isotropic plate with a negative Poisson's ratio

Vibrations of viscoelastic isotropic rectangular plates of an auxetic metamaterial are considered in a linear formulation. The problem is described by a linear integro-differential partial differential equation with initial and boundary conditions. The weakly singular relaxation kernel of Koltunov-R...

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Bibliographic Details
Published in:Stroitel'stvo unikal'nyh zdanij i sooruhenij 2022-05 (7), p.1-1
Main Authors: Abdikarimov, Rustamkhan Alimkhanovich, Vatin, Nikolai Ivanovich, Khodzhaev, Dadakhan
Format: Article
Language:English
Subjects:
Boundary conditions
Free vibration
Galerkin method
Kernels
Metamaterials
Numerical methods
Partial differential equations
Poisson's ratio
Quadratures
Rectangular plates
Time functions
Viscoelasticity
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Summary:Vibrations of viscoelastic isotropic rectangular plates of an auxetic metamaterial are considered in a linear formulation. The problem is described by a linear integro-differential partial differential equation with initial and boundary conditions. The weakly singular relaxation kernel of Koltunov-Rzhanitsyn is used. Using the Bubnov-Galerkin method, the resulting equation is reduced to a linear ordinary integrodifferential equation with respect to the time function. This equation is solved by a numerical method based on the use of quadrature formulas, eliminating singularities in the relaxation kernel. The effect on the amplitude-frequency characteristic of vibrations of a viscoelastic isotropic rectangular plate of a metamaterial with a negative Poisson's ratio is studied.
ISSN:2304-6295
DOI:10.4123/CUBS.105.02