Approximate Calculation of the Natural Oscillation Frequency of the Vibrating Table in Inter-Resonance Operation Mode

Abstract

Abstract The first natural frequency of oscillations of the vibrations of a discrete-continuous interresonant vibrating table plate was found using the functions of the Krylov-Duncan. The continuous member, presented in a plate hinged at four points, is used as a reactive mass with distributed parameters to create an inter-resonance vibrating table with an electromagnetic drive. For this purpose, the plate was considered as a rod on hinged supports. The justification of this approach is confirmed by simulation in the Ansys software. The results were confirmed using the approximate Rayleigh-Ritz method. The geometric shape of the plate is reduced to a section of a hyperboloidal surface. The results of simulation of the first natural frequency were verified experimentally.