Dynamics of deformable flexible systems in liquid

Abstract

The state-of-the-art in the investigation of nonlinear oscillations and evolution of deformable flexible systems in fluid is analyzed. Statements of problems and methods of solving them as well as results on the dynamics of flexible systems interacting with the ambient medium are briefly outlined. Important quantitative and qualitative results are presented, and conclusions of applied and fundamental importance are drawn Introduction. The need for theoretical analysis of the dynamic deformation of extended flexible branched systems that interact with the ambient medium arises in oceanographic research and marine engineering [23,25,36,43,47,51,52,67,80], in space technology and aeronautical engineering [2,3,38,69], in the oil and gas industry, in high-rise construction (bridges, masts, towers, pylons [4, 5, 7]), etc. Of widespread use are floating craft of various purposes anchored at depths of hundreds of meters and even kilometers and distributed-parameter structures towed in water (seismic streamers, rig pipelines, oil booms, etc.). To ensure their positioning, stability, and reliability, the structure of floating drilling rigs and submarine communication systems widely employ cable systems. The flexible elements of extended structures are subject to nonuniformly distributed loads and can be arbitrarily fixed at the ends. The specific behavior of flexible elements is that they can only be stretched, but not compressed. One of the problems associated with the operation of extended flexible structures is slacking and jerking of cables caused by external factors (wind, waves, current, forces). Variable forces and jerks acting for a long time adversely affect the strength and reliability of such structures. To abate the effect of jerks, nonlinear elastic and viscoelastic cables are employed. To assess the life of flexible elements, we need data on their stress state, displacements, amplitude-frequency characteristics, etc. Conducting relevant experiments would be difficult and expensive.The efficiency and reliability of solving three-dimensional nonstationary nonlinear dynamic problems for flexible branched systems interacting with the ambient medium greatly depends on the description of the viscoelastic and nonlinear elastic behavior of such systems, discretization methods, and methods and algorithms of solving initial-boundary-value problems. Various aspects of the dynamics of such systems are addressed in the monographs [3, 5, 24, 31, 33-35, 50, 57, 59] and the reviews [2,6,32,38,45,49,71,75,76], which is indicative of much practical and theoretical interest in such problems.The mechanics of slender columns and cables in flows has a history reaching back over a century. Of the early studies on the static behavior of a cable-body system in a fluid, noteworthy is Krylov's paper [42] which gives an analytic formula for tension and an integral representation of equilibrium. The dynamics of such systems has been studied to mach lesser extent than their statics. A literature review reveals considerable diversity in ...