We developed the nonlinear model of pipeline dynamics with high-speed liquid motion. On the basis of the variational methods we constructed the nonlinear discrete model and numerical algorithm for investigation of problems of dynamics and dynamical stability of pipeline. We considered examples of dynamical behavior of the system for different velocities of liquid flowing, including the case of critical velocity of flow, when loss of straight line stability of pipeline is possible. | Vietnam Journal of Mechanics, VAST, Vol. 30, No. 4 (2008), pp. 281 – 290 Special Issue of the 30th Anniversary NONLINEAR DYNAMICS OF PIPELINE WITH LIQUID IN A VICINITY OF CRITICAL FLOW VELOCITIES O. Limarchenko, Yu. Vasilevskiy Kiev National University, Ukraine Abstract. We developed the nonlinear model of pipeline dynamics with high-speed liquid motion. On the basis of the variational methods we constructed the nonlinear discrete model and numerical algorithm for investigation of problems of dynamics and dynamical stability of pipeline. We considered examples of dynamical behavior of the system for different velocities of liquid flowing, including the case of critical velocity of flow, when loss of straight line stability of pipeline is possible. Pipeline with flowing liquid is considered as a system, which consists of elastic pipeline and liquid. We consider that longitudinal motion of liquid is given, liquid is ideal and pipeline is modeled on the basis of beam theory. The objective of the article is development of nonlinear model of dynamics of pipeline with liquid and analysis of its validity on reflection of system behavior for different liquid flow velocities, including the domain of critical velocities, when loss of straight-line shape of pipeline is manifested. This model is aimed at investigation of the system behavior on transient motion. In particular such class of problems is of interest for modeling transient motions of pipelines for accidental break of pipelines, for damping vibrations of pipelines. Construction of mathematical model of the system is done on the basis of the Hamilton-Ostrogradskiy variational principle. It is necessary to note that on the use of this variational principle some methodical difficulties originate due to mixed description of motion of system components, namely, lquid motion is considered in the Euler variables and beam motion is described in the Lagrange variables. At the same time total motion of liquid particles .
