In this paper, a conjugate spectral problem and
biorthogonality conditions for the problem of extended plates of variable
thickness are constructed. A technique for solving problems and numerical
results on the propagation of waves in infinite extended viscoelastic plates of
variable thickness is described. The viscous properties of the material are
taken into account using the Voltaire integral operator. The investigation is
carried out within the framework of the spatial theory of viscoelasticity. The
technique is based on the separation of spatial variables and the formulation
of a boundary value problem for Eigen values which are solved by the Godunov
orthogonal sweep method and the Muller method. Numerical values of the real and
imaginary parts of the phase velocity are obtained depending on the wave
numbers. In this case, the coincidence of numerical results with known data is
obtained.

Cite this paper

Safarov, I. I. and Boltaev, Z. I. (2018). Propagation of Natural Waves on Plates of a Variable Cross Section. Open Access Library Journal, 5, e4262. doi: http://dx.doi.org/10.4236/oalib.1104262.

Kravchenko, V.T. and Myaleshka, V.V. (1981) Properties of Harmonic Waves Propagating along the Edges of the Rectangular Elastic Wedge. Akustik Journal, 27, 206-212.

Safarov, I.I., Akhmedov, M.S. and Rajabov, O. (2015) Vibrations of Plates and Shells with Attached Concentrated Mass. Lambert Academic Publishing, Saarbrücken, 92 p.

Safarov, I.I., Akhmedov, M.S. and Boltayev, Z.I. (2015) Dissemination Sinusoidal Waves in of a Viscoelastic Strip. Global Journal of Science Frontier Research: F Mathematics and Decision Sciences, 15, 39-60.