Establishing the natural frequency of oscillations of a continuous system with a concentrated mass in aviation and manufacturing engineering

The uneven transportation of products in the working bodies (trays) of one-mass vibrating conveyors with inertial exciters prompted the conduct of a study aimed at establishing the natural frequency of oscillations of a continuous system, namely, a long-dimensional body with distributed parameters in the form of a beam with a rigidly fixed concentrated mass. Using the Krylov-Duncan functions, the differential equation of movement of the beam was solved, taking into account the concentrated mass and the boundary conditions at its ends. The system of equations made it possible to analytically establish the natural frequency of such a continuous system. This approach was tested to establish the natural oscillation frequency of a glider, demonstrating its versatility for use in various industries. An analysis of the obtained results was carried out, and conclusions were drawn.