ISJ Theoretical & Applied Science 10(90) 2020

Philadelphia, USA

Safarov, I. I., Ishmamatov, M. R., Kulmuratov, N. R., & Маrasulov, A. M.

Natural oscillations of viscoelastic conical shell.

Full Article: PDF

Scientific Object Identifier: http://s-o-i.org/1.1/TAS-10-90-41

DOI: https://dx.doi.org/10.15863/TAS.2020.10.90.41

Language: English

Citation: Safarov, I. I., Ishmamatov, M. R., Kulmuratov, N. R., & Маrasulov, A. M. (2020). Natural oscillations of viscoelastic conical shell. ISJ Theoretical & Applied Science, 10 (90), 237-242. Soi: http://s-o-i.org/1.1/TAS-10-90-41 Doi: https://dx.doi.org/10.15863/TAS.2020.10.90.41

Pages: 237-242

Published: 30.10.2020

Abstract: In this article, the integral-differential equations of natural vibrations of a viscoelastic truncated conical shell are obtained on the basis of the shell equation. Geometrically nonlinear mathematical models of deformation of conical shells are obtained, taking into account the rheological properties of the material. Based on the method of variable separation, a method for solving and an algorithm for equations of natural vibrations of a viscoelastic truncated conical shell with pivotally and freely supported edges is developed. The problem is reduced to solving homogeneous algebraic equations with complex coefficients of large order. For a solution to exist, the main determinant of a system of algebraic equations must be zero. From this condition, we obtain a frequency equation with complex output parameters. The study of natural vibrations of viscoelastic truncated conical shells is carried out and some characteristic features are revealed. The complex roots of the frequency equation are determined by the Muller method. at each iteration of the Muller method, the Gauss method is used with the main element highlighted. As the number of edges increases, the real and imaginary parts of the natural frequencies increase, respectively. Taking into account the rheological properties of the material allows you to increase the frequency values of the shell up to 10%.

Key words: conical shell panel, the non-linear model, the oscillations of visco elasticity, the frequency equation, the frequency.