Investigations of Vibrations in the Complex Dynamical Systems of Transmission Pipelines
Mathematical models for complex dynamical systems of transmission pipelines with distributed and discrete parameters are formulated in this paper, which consist of a partial differential equation and nonlinear boundary conditions. The approximate analytical method of small parameter is developed for investigation of vibrations in the considered systems. The conditions of vibrations self-excitation were obtained in analytical form as well as a formula for amplitudes of possible vibrations. It is shown that it is possible to change purposefully frequencies and amplitudes of vibrations and avoid an excitation of undesirable vibration processes, including self-excited vibrations.
KeywordsDiscrete Parameter Nonlinear Boundary Condition Complex Dynamical System Nonconservative System Approximate Analytical Method
Unable to display preview. Download preview PDF.
- 1.Philipov, A.P.: Oscillations of Mechanical Systems [in Russian]. Kiev, Naukova Dumka (1965) 706.Google Scholar
- 2.Kuhta, K.Y., Kravchenko, V.P., V.A. Krasnoshapka, V.A.: Qualitative Theory of Controlled Dynamical Systems with Distributed and Discrete Parameters [in Russian]. Kiev, Naukova Dumka (1986) 224.Google Scholar
- 3.Mul, E.V.: On Conditions of Excitation of Self-Oscillations in a Nonconservative Dynamic System with Distributed Parameters. Cybernetics and Computing Technology, Complex Control Systems, New York, Allerton Press, Inc., 111 (1998) 70–72.Google Scholar
- 4.Svetlitskiy, V.A.: Pipe-Lines and Hoses Mechanics [in Russian]. Moscow, Mashinostroenie (1982) 279.Google Scholar
- 5.Kravchenko, V.P., Mul, E.V., Shut M.I.: Possibilities to Control Oscillations in Systems of Machine Units with Distributed and Discrete Parameters [in Russian and in English]. Moscow, Mekhanika Kompozitsionnykh Materialov i Konstruktsii Vol. 5 4 (1999) 77–86.Google Scholar