Modeling of Vibration Mechanisms for Treatment of Granular Media
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MODELING OF VIBRATION MECHANISMS FOR TREATMENT OF GRANULAR MEDIA A. T. Vasyukova,1 V. N. Denisov,2 and S. P. Kurilin2
UDC 631.363.7
A study of the amplitude-frequency characteristics of working bodies taking the form of thin rectangular plates working in a granular medium is presented. Results were obtained for the case of elastic oscillations having large deflections using Bolotin’s asymptotic method. The solution to the problem is obtained in the form of Jacobi elliptic functions. The amplitude-frequency characteristics of the vibration mechanism’s plate working body are given for various specific gravity coefficient values. A “pseudofluid” model is adopted as a simulated granular medium. An “attached mass” model is used to estimate the influence of the granular medium on the amplitude-frequency characteristics. Keywords: vibration mechanism, plate, nonlinear oscillations, amplitude-frequency response, granular medium, attached mass.
One of the most important methods currently used for intensifying technological processes involving materials at oil production and refining enterprises, as well as in chemical, construction, and other industries, is vibration treatment. Various vibration treatments are used to increase the efficiency of equipment, improve the characteristics of technological processes, reduce operating costs, and improve product quality [1–4]. In this connection, one of the latest areas of research and practical interest consists in the development of vibration mechanisms driven by linear induction motors for the treatment of granular media. A number of existing vibration mechanism designs are already protected by patents of the Russian Federation [5–7]. However, in order to ensure continuing development in this promising field, a more detailed study on the interaction of elements operating with a granular medium is required. To this end, a “fluidized medium” model can be used whose parameters are determined by the frequency and amplitude of the transverse vibrations provided by the operating element [4, 8]. In order to reliably determine such parameters, it is necessary to carry out resonance state studies of the operating elements of the mechanism. The operating elements of vibration mechanisms are often made in the form of plates or thin shells vibrating in a granular medium. Under the influence of vibrations, the physical properties of the medium change in terms of increased homogeneity and fluidity [4, 8]. In this way, the vibration effects ensure a significant reduction in the energy consumption of the mechanism during technological processes. At the same time, operation at resonant frequencies also contributes to the selfcleaning of the mechanism working surfaces, therefore leading to a further reduction in energy consumption and increased efficiency of the mechanism. In this case, it is necessary to ensure the strength and reliability of the operating elements in the vibration mechanisms. The present paper represents some of the results of the author’s studies on the resonant (natural) freq
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