The vibrations of deformed bodies interacting with
an elastic medium are considered. The
problem reduces to finding those values of complex Eigen frequencies for which
the system of equations of motion and the radiation conditions have a nonzero
solution to the class of infinitely differentiable functions. It is shown that
the problem has a discrete spectrum located on the lower complex plane and the
symmetric spectrum is an imaginary axis.
Cite this paper
Safarov, I. I. , Teshaev, M. K. and Boltayev, Z. I. (2018). Own Vibrations of Bodies Interacting with Unlimited Deformable Environment. Open Access Library Journal, 5, e4432. doi: http://dx.doi.org/10.4236/oalib.1104432.
Safarov, I.I., Akhmedov, M.S. and Boltaev, Z.I. (2015) Distribution of the Natural Waves of Extended Lamellar Viscoelastic Bodies of Variable Thickness. LAP, Lambert Academic Publishing, Saarbrücken, 112 р.
Mayboroda, V.P., Troyanovsky, I.E. and Safarov, I.I. (1983) Free and Forced Oscillations of Systems of Solids on Inhomogeneous Viscoelastic Shock Absorbers. Journal Academy of Sciences, 3, 71-77.
Safarov, I.I., Teshaev, M.X., Akhmedov, M.S. and Boltaev, Z.I. (2017) Properties of Wave Motion in a Cylindrical Shell Is Contact with a Viscous Fluid. Case Studies Journal, 6, 9-35. http://www.casestudiesjournal.com
Safarov, I.I., Teshaev, M.Kh., Boltaev, Z.I. and Nuriddinov, B.Z. (2017) Of Own and Forced Vibrations of Dissipative Inhomogeneous Mechanical Systems. Applied Mathematics, 8, 1001-1015. http://www.scirp.org/journal/am https://doi.org/10.4236/am.2017.87078
Safarov, I.I., Akhmedov, M.Sh. and Boltaev, Z.I. (2015) Setting the Linear Oscillations of Structural Heterogeneity Viscoelastic Lamellar Systems with Point Relations. Applied Mathematics, 6, 225-234. http://www.scirp.org/journal/am https://doi.org/10.4236/am.2015.62022
Safarov, I.I., Akhmedov, M.Sh. and Boltayev, Z.I. (2015) Dissemination Sinusoidal Waves in of a Viscoelastic Strip. Global Journal of Science Frontier Research: F Mathematics & Decision Sciences, 15, 39-60.
Bozorov, M.B., Safarov, I.I. and Shokin, Yu.I. (1986) Numerical Simulation of Oscillations of Dissipative Homogeneous and Inhomogeneous Mechanical Systems. Siberian Branch of the Russian Academy of Sciences, Novosibirsk, 188 p.
Safarov, I.I., Teshayev, M.K., Boltayev, Z.I. and Akhmedov, M.Sh. (2017) Damping Properties of Vibrations of Three-Layer VIscoelastic Plate. International Journal of Theoretical and Applied Mathematics, 3,191-198. http://www.sciencepublishinggroup.com
Safarov, I.I., Akhmedov, M.Sh. and Rajabov, O. (2017) About the Natural Oscillations Viscoelastic Toroidal Shell with the Flowing Fluid. World Wide Journal of Multidisciplinary Research and Development, 3, 295-309. http://www.wwjmrd.com
Safarov, I.I., Akhmedov, M.Sh. and Boltaev, Z.I. (2015) Natural Oscillations of Cylindrical Bodies with External Friction on the Boundary. Applied Mathematics, 6, 629-645. http://www.scirp.org/journal/am https://doi.org/10.4236/am.2015.63057
Safarov, I.I., Kuldashev, N.U. and Ochilov, Sh.B. (2017) Numerical Solution of the Problem of the Impact a Plane Stationary Elastic Waves by a Cylindrical Body. Case Studies Journal, 6, 192-213. http://www.сasestudisjournal.com