4 research outputs found
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