On Asymptotical Method for Vibrations Analysis of Large Elastic Dynamical Systems

Abstract:
Large elastic dynamical systems are widespread in heavy, extractive and manufacturing industry as well as in space-system engineering. Intensive vibrations in such systems are possible but they are not admissible by systems specifications. Before such systems were usually modelled with a help of ODE's that caused significant discrepancies in results of investigations and vibrations control. In this paper more exact model is used for a real large flexible elastic dynamical system, which is
considered as a system with distributed and discrete parameters. This mathematical model is a non-classical boundary value problem in PDE's. The problem complexity results in impossibility to find its exact solution. Therefore an asymptotical method is used for investigations. The conditions at which vibration processes of different character take place in the considered dynamical systems are defined. Also the formula for determination of frequencies of possible vibrations is obtained. Influence of different parameters of the dynamical systems on vibrations frequencies is analyzed. For the purpose of active control of vibrations it is proposed to use some determined feedbacks in the considered systems.

The research of Olena Mul was supported by FCT, fellowship SFRH/BPD/14946/2004.