Development of an analysis-synthesis method for designing single degree of freedom nonlinear dynamical systems

Abstract

Based on the resonant frequencies of a nonlinear dynamic system and the magnitude of the system excitation force, a new analysis-synthesis method has been developed that allows the design of new nonlinear dynamic systems, specifying zones of minimal vibrations and stable operating modes. The operating mode frequency zone has been determined, in which a sudden change in the size of vibrations leading to unstable operation of the system is possible. The boundaries of minimum vibration and stable operating frequency zones are determined. It is shown that the developed analysis-synthesis method allows designing a nonlinear dynamic system with low vibration level and stable operation, evaluating the features of the interaction between the values of the main parameters of the system and the excitation frequencies of the operating modes by analyzing them. Cases have been clarified when the use of a damper in a nonlinear dynamic system will not reduce, but only increase the level of vibrations in it. The accuracy of the analysis methods presented in the article was verified by numerical calculations.