About vibrations of the inertial screen frame

Abstract

In the previous work “On Inertial Screens,” I considered a vibrating screen as a system with three degrees of freedom, which corresponds to the assumption of the symmetry of all the masses of the screen and the forces applied to them relative to a certain vertical plane of symmetry intersecting with the screen sieve along the line of its greatest slope. The general case of small oscillations of an inertial screen, considered as a rigid body with all 6 degrees of freedom, is analyzed, and the conditions under which the problem can be reduced to three degrees of freedom are clarified (the case discussed in the previous article - “On inertial screens”). Euler's equations that determine the motion of a rigid body are simplified due to the smallness of its vibrations, and in a first approximation the problem is reduced to solving the System of 6 aggregate linear equations with constant coefficients or even to individual linear equations. If necessary, the result can be improved by successive approximation, also taking into account nonlinear terms."