ISJ Theoretical & Applied Science 12(80) 2019

Philadelphia, USA

Safarov, I. I., Тeshaev, M. K., Boltaev, Z. I., Kulmuratov, N. R., & Hamroev, N. N.

Own waves in a spatial viscoelastic cylinder with radial crack.

Full Article: PDF

Scientific Object Identifier: http://s-o-i.org/1.1/TAS-12-80-67

DOI: https://dx.doi.org/10.15863/TAS.2019.12.80.67

Language: English

Citation: Safarov, I. I., Тeshaev, M. K., Boltaev, Z. I., Kulmuratov, N. R., & Hamroev, N. N. (2019). Own waves in a spatial viscoelastic cylinder with radial crack. ISJ Theoretical & Applied Science, 12 (80), 341-345. Soi: http://s-o-i.org/1.1/TAS-12-80-67 Doi: https://dx.doi.org/10.15863/TAS.2019.12.80.67

Pages: 341-345

Published: 30.12.2019

Abstract: This work considers the propagation of natural waves by an infinite viscoelastic cylinder with a radial crack. The task is posed in cylindrical coordinate systems. Using the Navier equation and the physical equation, a system of six differential equations is obtained. After not complicated transformations, a spectral boundary-value problem was obtained for a system of ordinary and partial differential equations with complex coefficient equations, which is further solved by the direct and orthogonal Godunov sweep method with a combination of the Mueller and Gauss methods. The dispersion relation is obtained for a viscoelastic cylinder with a radial crack. It was found that, in the case of a cylinder with a radial crack, the first mode has a cutoff frequency, and the phase velocity tends to infinity. At large wavenumbers, the limiting phase velocity of this mode coincides with the velocity of the Rayleigh wave. At the cutoff frequency, the axial displacements are equal to zero and the oscillations of the cylinder occur in a plane deformed state.

Key words: crack, viscoelastic cylinder, freezing procedure, Navier equation, orthogonal sweep, ordinary differential equation.