The book is written for students of universities and postgraduate students specializing in the field of nonlinear dynamics, as well as specialists in various fields of mechanical engineering. It is devoted to the development of original methods, and outlines the results of analytical studies of dynamical chaos, synchronization, and dynamic structures in lattices of coupled rotators. It presents its findings within the context of the phase space of models and by involving methods of the qualitative theory of differential equations, the theory of bifurcations, and qualitative numerical methods. ... Read more

Extractable deposits of silver, gold, copper, zinc, lead, gas hydrates and other valuable materials can be found at the ocean floor. The most valuable minerals are found at large depths, starting from 1000 m and deeper. Therefore, the leading offshore companies are currently designing systems and tools for deep sea mining. The mining at the desired depth of a few kilometers is a great challenge though as it has never been attempted before at the commercial scale. One of the fundamental design challenges lays in the understanding of and preventing from the problems associated with the dynamics of a subsea Vertical Transport System (VTS). The function of the VTS is to transport slurry (a thin mixture of water and finely divided minerals) from the seafloor to the mining support vessel. The VTS consists of a vertically hanging submerged pipe through which the slurry is transported upwards and a number of booster stations which maintain the pressure in the pipe that enables the desired slurry flow. The VTS system is subject to a number of the dynamic excitations such as the vessel motion, the slurry flow in the pipe, the sea current and a propulsion device that is envisaged to control the position of the lower end of the pipe at the desired location. To design a reliable VTS system the effect of all the above-mentioned excitation mechanisms has to be accounted for. ... Read more

This paper studies the conditions for existence and stability of stationary cluster structures in lattices of diffusively coupled dynamical systems within the framework of a new interpretation of cluster synchronization as classical synchronization of cluster oscillators (C-oscillators). The study of existence of cluster attractors is based on the linear chains of cluster oscillators, defining possible types of cluster structures in chains. First, we present interval estimates for the range of coupling strengths in which cluster attractors can exist. Then we formulate and prove the basic theorems about the local stability of the various cluster structures. The presented methodology can be extended to study cluster structures on lattices of different geometry and forms such as linear cluster structures in two-dimensional lattices, layered cluster structures in three-dimensional lattices and cluster structures in ring-shaped systems. Crown ... Read more

Dynamics of pipes conveying fluid represents quite an old problem. The first references to the empirical observations are dated 1885 [1]. The first published results of study of the dynamics of pipes conveying fluid belong to Bourrières and dated 1939 [1]. Most of the studies related to this topic are devoted to the case of pipe discharging fluid [2] while the case of the pipe aspirating fluid received less attention [1]. The interest to this topic is basically dictated by industrial needs. In particular, pipes aspirating fluid are planned to be used in the offshore industry being an integral part of the cooling system of gas-liquefying floating platforms. Early experiments conducted in the past did not show any instability that has been predicted theoretically until Kuiper et al carried out an experiment that demonstrated that the pipe can be unstable [1,3]. However, no explanation has been found so far as to the particular features of the observed instability, namely for the alternation between a nearly periodic orbital motion and a small noise-like vibration near the equilibrium. Also, it remained unclear why for two similar sets of the experiments carried out with the time delay of about one month, the amplitude of orbital motion was quite different (~0.25 and ~1.5 pipe diameters, respectively). None of the existing theories is capable to predict the alternating motion. Thus, one still needs to answer the following questions: what is the physical origin of the observed dynamics? What could cause such a difference in the amplitude of the orbital motion in two identical experiments? This report presents an attempt to answer these questions. ... Read more