  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.
