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.
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