Dynamic Properties of a Dispersed Material under Harmonic Vibrations

The aim of the work is to establish the dynamic properties of a dispersed material with harmonic vibrations. In strength calculations of structural elements of aircraft, among other things, modes of forced and natural vibrations are taken into account. In this regard, the dynamic properties of the transported cargo are taken into account, which are significantly different for solid and dispersed materials. The research methodology consists in presenting the status of the system under study as a combination of its diametrically opposite limiting statuses. Considered is a dispersed material located on a platform that performs harmonic vibrations. To assess the instability (or stability) of a dispersed material relative to the platform, a dimensionless quantity \(\xi \) is introduced. Its limiting values are \({{\xi }_{a}}\) —absolute stability (complete immobility) relative to the platform and \({{\xi }_{z}}\) —absolute instability. The main problem in establishing the dynamic properties of a dispersed 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 dispersed material in the form of a composition of its unstable and stable statuses provides the key to solving this (and similar) problems. Opposite limit statuses of the system under study can be comparable and incomparable in terms of quantitative assessment. The subjects of the study are systems with equal limiting statuses. The proposed method is universal and applicable to a wide variety of systems with different statuses and parameters.