Approximate calculation of natural frequencies of oscillations of the diamond-shaped plates of the discrete-continuous inter-resonance vibrating table

Abstract

Abstract Conventional single- and two-mass vibrating machines do not have a sufficient level of energy efficiency. There are vibration machines based on inter-resonance oscillating systems, which make possible the significant reduction in the use of electricity. To implement highly effective inter-resonance operation modes of vibrating machines, the oscillating masses of such a system must precisely calculate values of inertial-rigid parameters, as well as their frequency of oscillations. Since the synthesis of continuous sections into classical discrete models of multi-mass mechanical oscillating systems has recently become widespread, the most optimal option is to use a continuous member as a reactive mass of a vibrating machine. The continuous member combines inertial and stiffness parameters and makes it extremely easy to perform the reactive mass. In particular, rectangular plates are used as continuous members. The rectangular shape of the plate is not the only option for making a continuous member. This paper proposes the construction of a discrete-continuous inter-resonance vibration machine with electromagnets, where a diamond-shaped plate is used as a continuous member. The authors carried out the computation of the first natural frequency of the diamond-shaped plate using the Rayleigh-Ritz method with the equation of the hyperboloid. The determined eigenfrequency was confirmed in the Ansys software.