Dynamic instability of vibrations of thin-wall composite curvorine viscoelastic tubes under the influence of pulse pressure

¹ Department of Theoretical and Constructional Mechanics, Tashkent Institute of Irrigation and Agricultural Mechanization Engineers, 39 KoriNiyoziy str., Tashkent 100000, Uzbekistan
² Tashkent Institute of Chemical Technology, 32 Navoi st., Tashkent 100000, Uzbekistan
³ Bukhara Engineering-Technological Institute, 15 K. Murtazaev str., Bukhara 200100, Uzbekistan.

^* Corresponding author: theormir@mail.ru

Abstract

In this paper the results of a study of the dynamic characteristics of thin-walled composite curved viscoelastic pipes under the influence of internal pulsating pressures is presented. The relationship between stress and strain is described by the Aviary equations. Based on the principle of calculus of variations, the equations of the dynamics of curvilinear shells are obtained. The obtained integral and integro-differential equations are solved using the finite element method, the Mueller and Gauss methods. The results of calculations of the natural frequencies of the shell and the curved rod are compared. As a result of the calculation, it was found that, shell vibrations occur at higher frequencies than rod vibrations (manifestation of a boundary effect). With this difference, the natural frequency, which has no analogue in the rod model decreases. This is due to the fact that, in this case the transverse vibrations of the section itself become significant, the rod. Some mechanical effects were discovered when taking into account the rheological properties of the pipe material.