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Plane waves and problems of steady vibrations in the theory of viscoelasticity for Kelvin-Voigt materials with double porosity

Svanadze M. M.

Archives of Mechanics

2016

Vol. 68, nr 6

441--458

In the present paper the linear theory of viscoelasticity for Kelvin–Voigt materials with double porosity is considered. Some basic properties of plane harmonic waves are established and the boundary value problems (BVPs) of steady vibrations are investigated. Indeed on the basis of this theory three longitudinal and two transverse plane harmonic waves propagate through a Kelvin–Voigt material with double porosity and these waves are attenuated. The basic properties of the singular integral operators and potentials (surface and volume) are presented. The uniqueness and existence theorems for regular (classical) solutions of the BVPs of steady vibrations are proved by using the potential method (boundary integral equations method) and the theory of singular integral equations.

Electromagnetic scattering by a periodic array of thick-walled parallel plate waveguides

Tasinkevych Y.

Journal of Technical Physics

2009

Vol. 50, no 1

41-53

Electromagnetic wave scattering by a periodic array of semi-infinite thick-walled parallel plate waveguides is studied in this paper. The cases of TE and TM polarization of an incident plane harmonic wave are considered separately. The scattered field above the waveguides is sought in the form of a series of spatial harmonics in accordance with the Floquet's theorem, whereas in the waveguide regions it is sought in the form of parallel plate waveguide modes. To satisfy the boundary and edge conditions by field components in the free space above the array, the Fourier expansion for spatial harmonics amplitudes with corresponding coefficients, being properly chosen Legendre functions, is exploited. The unknown coefficients are the solutions of certain doubly infinite systems of linear equations. The approximate solution is found numerically.