Analysis of vibrations in large flexible hybrid systems

Abstract

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 makes it impossible to find exact analytical solutions. To address the problem, we use the asymptotical method of small parameters 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 characteristics take place, are defined. The dependence of the vibration frequencies on the physical parameters of the hybrid system is studied. We show that introduction of different feedbacks into the system allows one to control the frequency spectrum, in which excitation of vibrations is possible.