Natural and forsed osculations of pipelines in contact with the Wincler medium

¹ Tashkent Institute of Chemical Technology, 32, Navoi str., Tashkent, 100011, Uzbekistan
² Bukhara branch of the Institute of Mathematics named after V.I. Romanovsky, 11, M.Iqbol str., Bukhara, 105017, Uzbekistan
³ Bukhara Institute of Engineering and Technology, 15, K. Murtazayev str., Bukhara, 105017, Uzbekistan
⁴ Asia International University, 74, Gijduvan str, Bukhara, 105026, Uzbekistan
⁵ Bukhara State University, 11, M.Iqbol str., Bukhara, 105017, Uzbekistan

^* Corresponding author: muhsin_5@mail.ru

Abstract

In this paper, the pipeline is modeled as a curved rod in contact with the Winkler medium. Linear oscillations of a curved viscoelastic rod lying on the Winkler base are considered. The general formulation of the problem of free oscillations of a spatially curved viscoelastic rod with variable parameters is reduced to a boundary value problem for a system of ordinary integro-differential equations of the 12th order with variable coefficients relative to eigenstates; it can be solved by the method of successive approximations. The relations allowing to present the solution of the boundary value problem for the rod in an analytical form are formulated. It is established that the dimensionless complex frequencies of natural oscillations of a spatially curved rod, while maintaining the elongation of the rod constant, do not depend on it. The Poisson's ratio has little effect on the dimensionless real and imaginary parts of the natural frequencies.