On the inertial screens
Abstract
Starting from the consideration of the oscillating inertia screen as a system with three degrees of freedom, a system of Lagrange's differential equations is formed, and the small terms depending on the translatory and Coriolis acceleration of the inertia weight are omitted. The design of the screen in which the resulting equations become independent and the torsional vibrations almost disappear is described. In order to amplify the vibrations of the screen perpendicular to its plane, the system should be tuned to resonance with these vibrations. Assuming that the oscillations of the inertia screen take place perpendicular to the plane of the screen, the motion of an inelastic particle jumping along the screen is analyzed, and the resonance conditions between the screen oscillations and the particle jumps are determined. It turns out that the screen of slate rock "resonance" also quite well satisfies the condition of this second resonance. The condition for the existence of complete resonance is investigated, and the motion of inelastic particles under complete and incomplete resonance is analyzed. Formulas are given for calculating the efficiency of the screen and the sum of the kinetic energies of all impacts of a given particle during its motion along the screen under complete resonance. For incomplete resonance, an example of numerical calculation is provided.
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References
- S.P. Timoshenko, Theory of Oscillations in Engineering, pp. 34, 35 (in Russian)
- L.G. Loitsyanskii and A.I. Lurye, Theoretical Mechanics, Part III, pp. 349, 353 (in Russian)
- S.P. Timoshenko, Theory of Oscillations in Engineering, p. 34
- L.G. Loitsyansky and A.I. Lurye, Theoretical Mechanics, Part III, p. 353