Расчет ускорений колоса при взаимодействии растения с мотовилом
Calculation of ear accelerations when interacting with a reel

On the basis of the well-known analytical solution of the mechanics of a solid deformable body, the article deals with the problem of free vibrations of a cereal crop plant arising as a result of a transverse absolutely elastic impact on it with a reel bar. The geometric model of a non-deformed stem of a plant is presented in the form of a straight-line isotropic rod with a constant bending stiffness. The mass-geometric parameters of the spike, as well as the conditions of plant fixation, are taken into account in the form of boundary conditions. The solution of the free stem oscillation problem is performed on the basis of the calculation of the function of the elastic line of the rod, which is a well-known solution of a fourth-order differential equation written in partial derivatives. The analytical form of recording the movement of the elastic line of the stem is performed with the help of Krylov functions and Fourier series under certain conditions at the edge of the rod and the initial conditions of its movement. Solving the problem of free vibrations of the stem after an elastic collision with the reel bar made it possible to compute the speed and acceleration of the plant in the ear zone. In addition, the presented solution allows introducing into agricultural mechanics a new criterion for the stress of interaction between a rod and a plant. The criterion is in the calculation of the period of bending oscillations of the plant at the first frequency and the comparison of this value with the total time of interaction of the rod with the plant.