Browsing by Author "Maistruk, Pavlo"

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Approximate calculation of natural frequencies of oscillations of the plate with variable cross-section of the discrete-continuous inter-resonance vibrating table
(Видавництво Львівської політехніки, 2022-02-22) Lanets, Oleksii; Maistruk, Pavlo; Maistruk, Volodymyr; Derevenko, Iryna; Lviv Polytechnic National University
Problem statement. To ensure highly efficient inter-resonance modes of operation of vibrating equipment, the oscillating masses of the system must have certain inertia-rigid parameters, as well as a certain frequency of natural oscillations. The disadvantage of highly efficient inter-resonance oscillatory systems is that the third reactive mass must be small, and therefore the use of complex and large structures is impossible. Therefore, it is best to use the reactive mass as a continuous section. The continuous section, which is a flexible body, optimally combines inertial and rigid parameters. Scientific works have already considered the design of the vibrating table, in which the continuous section is an ordinary rectangular plate hinged in the intermediate mass. This decision looks quite promising. However, likely, the rectangular shape of the plate is not the best option to ensure maximum energy efficiency. Purpose. Extend the method of calculating the natural frequency of oscillations of the plates by the approximate Rayleigh-Ritz method using the general hyperboloid equation to plates with variable cross-section for the proposed types of plates and check the results with the calculation in Ansys software. Methodology. The calculations of the plates were performed using the basic principles of the theory of oscillations, in particular the Rayleigh-Ritz method in the software product MathCAD. Findings (results) and originality (novelty). Two types of elastic plates with variable cross-sections are considered. In the first case, the shape of the plate was given by quadratic functions, in the second case, it was described by trigonometric functions of cosine. In both cases, the same conditions of attachment in the intermediate mass were observed. The calculation of the first natural frequency of oscillations of the considered plates was performed using the approximate Rayleigh-Ritz method with the assumption that the deflection of the plates occurs on the surface of the hyperboloid. The reliability of the obtained results was verified by numerical calculation in the software product Ansys. Practical value. It is assumed that the proposed types of plates can increase the dynamic potential of the vibrating machine. Scopes of further investigations. For further study of the considered types of plates as a continuous section of the inter-resonance vibrating machine, it is necessary to calculate their deflections at forced oscillations.
Optimization of the shape and dimensions of the continuous section of the discrete-continuous inter-resonance vibrating table
(Видавництво Львівської політехніки, 2023-02-28) Maistruk, Pavlo; Lviv Polytechnic National University
Energy-efficient technologies are an important aspect of the development of mechanical engineering. Therefore, the creation of highly efficient vibration technological equipment is an urgent task. There are discrete-continuous inter-resonance vibration machines that have high values of dynamic amplification of oscillations. Rectangular plates or rods are used as the reactive mass of such vibrating machines. However, the rectangular shape of the plate may not be the optimal shape for achieving maximum energy efficiency. To conduct experimental studies of alternative plates with a variable cross-section to determine the optimal shape of the reactive mass of the vibration machine. Methodology. The selection of alternative options of plates with a variable cross-section, which would satisfy the necessary conditions of fastening and the value of the natural frequency of oscillations, was carried out. Experimental studies were carried out on a sample of an inter-resonance vibrating table. The value of the power supply voltage at which loads of different masses were separated from the working body of the vibrating table for each of the plate samples was compared. Findings (results) and originality (novelty). For the first time, experimental studies of the energy efficiency of inter-resonance vibration machines with plates with a variable cross-section installed as a reactive mass were conducted. It was found that the rhomboid shape of the plate is optimal when using it as a continuous section in a vibration machine with an electromagnetic drive. It was determined that the use of diamond-shaped plates as the reactive mass of the vibrating machine can improve the energy efficiency of the inter-resonance vibrating equipment. For further analysis of plates with a variable cross-section as a reactive mass of an inter-resonance vibration machine, it is necessary to calculate and compare their lumped inertia-stiffness parameters.