About dynamic stability of deformable elements of vibration systems

Abstract

The dynamics and stability of the elastic elements of vibration devices, modeled by a channel containing elastic elements, are investigated. Inside the channel flows a stream of stirred liquid. The model of the device with two elastic elements is considered. The solution of the aerohydrodynamic part of the problem, based on the methods of the theory of functions of a complex variable, is given. The solution of the original problem is reduced to the study of a coupled system of partial differential equations for the deformations of elements, which makes it possible to study their dynamics. On the basis of the constructed functional for this system, the sufficient conditions of stability are obtained. The conditions impose restrictions on the parameters of the mechanical system. Based on the Galerkin method, the numerical experiments for specific examples of mechanical systems were carried out, confirming the reliability of the investigations. A special case of the model of device with one elastic element is considered. Based on this case, a comparison with the model of the vibration device considered earlier is made.

Mathematical modeling in problems about dynamics and stability of elastic elements of wing profiles

“…Among the latter, we note the works [Abdelbaki et al, 2019;Blinkov et al, 2018;Butt et al, 2021;Chehreghani et al, 2021;Kheiri and Paidoussis, 2015;Kontzialis et al, 2017;Moditis et al, 2016;Mogilevich et al, 2017;Mogilevich et al, 2018;Mogilevich and Ivanov, 2020;Moshkelgosha et al, 2017] and many others. Among the works of the authors of this article on the study of the dynamics, stability and controllability of pipeline systems, we note the works [Gladun and Velmisov and Ankilov, 2016;Velmisov and Ankilov, 2017;Velmisov and Ankilov, 2018;Velmisov and Ankilov, 2019;Velmisov and Ankilov, 2021].…”

Investigation of dynamics of elastic element of vibration device

“…Среди исследований следует отметить работы [2,3,4,5,6,7,8] и многие другие. Среди работ авторов данной статьи по исследованию динамики и устойчивости упругих тел, взаимодействующих с потоком жидкости или газа, отметим монографии и статьи [9,10,11,12,13,14,15,16].…”