Известия Томского политехнического университета: Инжиниринг георесурсов (Sep 2017)
Investigation of nonlinear dynamics of structure components for oil refining and chemical industries
Abstract
The aim of the work is to study the nonlinear dynamics and complex mechanical contact interaction of beam-shell structures. The construction is under the action of the external load. The main properties of the structures, which components are the beam-shell structure, include: high wear resistance, resistance to various types of external influences. The study may help to improve these properties. The relevance. In view of the wide range of applications of the beam-shell structures in modern oil-refining and chemical industries the issues of nonlinear dynamics and complex contact interaction of beam-shell structures are relevant. The «pipe in pipe» type heat exchangers and tubing column can serve as the example of using such structures. Simulation and study of the dynamics of the beam-shell structures gives an idea about the impact of external and internal factors on operation of the objects under study. This allows predicting and controlling the operation of the described structures. The paper considers the construction of two nested closed cylindrical shells reinforced by a beam from the outside. There are gaps between the beam and the shell. The beam is subjected to the action of the transversal harmonic load. The problem is solved in three-dimensional statement, taking into account large deformation. The methods used in this study. The equations considering geometrically nonlinear structure and large deformation by V.V. Novozhilov in three-dimensional statement were taken as the initial equations for beam and shells. The contact pressure is determined by B.Ya. Kantor method. Partial differential equations for beams and shells are reduced to the Cauchy problem by the finite element method in the spatial variables. The Cauchy problem is solved by the explicit integration (Euler's method). The conservative structure was considered. The analysis was carried out by the methods of nonlinear dynamics and qualitative theory of differential equations: the authors have formed the signals, phase portraits, Poincare section, Fourier spectra, applied wavelet transform and analysis of signs of the Lyapunov exponents. The results and conclusions. The authors studied the frequency characteristics of the structural elements based on wavelet analysis and Fourier power spectra. The paper introduces the visualization of nonlinear vibrations of the structure elements. For the first time the chaotic phase synchronization phenomenon was defined for the described structure. The authors concluded on the preference of using wavelet analysis to study such systems. This method reveals the frequency characteristic of the system elements at each time.
