Klymenko A. Mathematical modeling of nonlinear oscillations of pendulum systems

The research subject is nonlinear vibration modes of pendulum systems and systems with pendulum absorbers. The goal is mathematical modeling of nonlinear vibration modes of pendulum systems, including several systems with pendulum absorbers with the numerical-analytical method. This method is based on the concept of nonlinear normal modes. The research methods are a method of nonlinear normal modes, the Rauscher method for analyze parametric and forced vibrations. It used methods that involve the Mathieu equation, Hill equation and Hill determinants, and some numerical-analytical approach of the stability analysis. The results can be used for numerical simulation of vibrations of machines, structures and facilities, having in its composition pendulum dampers. Scientific novelty lies in a new method of modeling the nonlinear normal modes of vibration of pendulum systems, providing research waveforms for both small and large amplitudes, including the study of stability and vibration modes in the application of numerical and analytical modeling method of parametric modess and forms of forced oscillation. The research results are planned to be introduced. Application branches are mechanical engineering and building industry.