Mizhidon A.   Barguev S.G.  

Research of the boundary problem for one hybrid system of the differential equations

Reporter: Mizhidon A.

Hybrid systems of the differential equations are understood as the system of the differential equations consisting of the ordinary differential equations and the equations in private derivatives. In work the hybrid system of the differential equations containing singularities of type   -functions is considered. Such class the hybrid system of the differential equations takes place at the description of dynamics of mechanical systems with the concentrated and distributed parameters (for example, the system of firm bodies installed on an elastic core, which ends are rigidly fixed). The concept of the generalized decision of hybrid system of the differential equations meeting boundary conditions, corresponding to rigid seal of a core is entered. Thus the class of the main functions can be treated as admissible variations of the generalized coordinates in principle Hamilton. The analitiko-numerical method of search of own frequencies and forms of fluctuations is offered. The decision of considered hybrid system of the differential equations is looked for by a method of division of variables. As a result the system of the amplitude equations turns out, and for firm bodies the algebraic equations, and for a core the linear differential equation of the fourth order with  - function in the right part with variable coefficient turn out. The substitution reducing this equation to the equation with   -function locates in the right part, but already with constant coefficient.Combining the decision initial the differential equation in points of fastening of firm bodies with the amplitude equations for firm bodies, the uniform algebraic system of the equations of rather unknown amplitudes turns out. From a condition of not triviality of the decision, the frequency equation turns out.