Inertial Properties of a Disperse Material in the Mode of Forced Oscillations

Abstract

It is noted that the modes of forced and natural oscillations are taken into account to calculate strength of structural elements of transport vehicles and mechanisms. In this regard, the dynamic properties of the transported cargo are considered, and they are significantly different for solid and disperse materials. 
 The study objective is to define the dynamic properties of a disperse material under harmonic vibrations. The research method is to present the status of the system under study in the form of a combination of its diametrically opposite maximum statuses. A common example of such a representation is the composition of a dry construction mixture – a combination of sand and cement (100% sand in the mixture is one maximum status, 100% cement is the diametrically opposite maximum status). A disperse material located on a platform performing harmonic oscillations is considered. To assess the instability (or stability) of the disperse material relative to the platform, a dimensionless quantity ξ is introduced. The main problem in determining the dynamic properties of a disperse material is the impossibility of calculating the average coefficient of dynamic friction, since its value is influenced by the interaction of dispersed particles with each other in the entire mass of the material, and not only with the surface of the platform. The description of the dynamic status of a disperse material as a composition of its unstable and stable statuses provides the key to solving this and similar problems. The opposite maximum statuses of the system under study may be comparable and incomparable in terms of quantitative assessment.
 The subject of the study are systems with equal maximum statuses. This method is universal and applicable to a wide variety of systems with different statuses and parameters.