Dynamics of Controlled Hybrid Systems of Aerial Cable-Ways

Dynamics of the hybrid systems of aerial cable-ways is investigated. The eigenvalue problems are considered for such hybrid systems with different assumptions. An overview of different methods for eigenvalue problems is given. In the research, the method of the normal fundamental systems is applied, which turns out to be very effective for the considered problems. Changes of dynamical characteristics of the systems depending on the controlled parameter are studied.Comment: Accepted (15-May-2006) to the Proceedings of the "International Conference of Hybrid Systems and Applications", The University of Louisiana, Lafayette, LA, USA, May 22-26 2006, to be published in the journal "Nonlinear Analysis: Hybrid Systems and Applications

Analysis of Vibrations in Large Flexible Hybrid Systems

The mathematical model of a real flexible elastic system with distributed and discrete parameters is considered. It is a partial differential equation with non-classical boundary conditions. Complexity of the boundary conditions results in the impossibility to find exact analytical solutions. To address the problem, we use the asymptotical method of small parameter together with the numerical method of normal fundamental systems of solutions. These methods allow us to investigate vibrations, and a technique for determination of complex eigenvalues of the considered boundary value problem is developed. The conditions, at which vibration processes of different character take place, are defined. Dependence of the vibration frequencies on physical parameters of the hybrid system is studied. We show that introduction of different feedbacks into the system allow one to control the frequency spectrum, in which excitation of vibrations is possible.Comment: Accepted for publication by the Global Journal of "Pure and Applied Mathematics". To be partially presented at the Sixth International Conference "Symmetry in Nonlinear Mathematical Physics", June 20-26, 2005, Institute of Mathematics, National Academy of Sciences of Ukraine, Kyiv (Kiev), Ukrain