Abstract
This paper presents the results of studying the dynamics of a vibration machine, takinginto account its interaction with the processing medium based on representing the medium as a continuoussystem. The application of the complex number method significantly simplifies the formation of equations ofmotion for the discrete-continuous system, which is a computational model of the vibration system "machinemedium."The study substantiates and develops a method for considering the mutual influence of the machineand the processing medium, based on representing the medium as a continuous system. The dynamicsof the vibration system "machine-medium" is studied, and oscillation parameters are determined withoutconsidering resistance forces. It is found that the overall motion of the vibration system is described by fourcomponents. The first three describe the natural oscillations of the system, of which the first two are determinedonly by initial conditions, and the third reflects the accompanying oscillations caused by the externalforce applied to the system. The last component defines the forced oscillations following the external force'schange law. This result shows that the oscillations of the vibration system are not strictly harmonic, which isconfirmed by the provided graphs. The dynamics of the "machine-medium" vibration system, consideringresistance forces, are studied, and analytical dependencies for determining oscillation amplitudes and natural and resonant frequencies are obtained. The results of the amplitude calculations of the vibration platform forvarious heights of compacted concrete mixtures reveal the influence of the resistance coefficient and theratio of oscillation frequency to the wave propagation speed in the mixture. Analysis of the obtained graphsshows that the resistance coefficient has a different effect on the amplitude of oscillations for different heightsof the compacting mixture. Certain mixture height zones of the vibration system "machine-medium" operatein a near-resonant mode. A significant influence on the amplitude is exerted by the wave propagation speed,which is included in the analytical formulas for determining the numerical values of the coefficients accountingfor reactive and active components of resistance.
Published Version
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