Approximate calculation of natural frequencies of oscillations of the plate with variable cross-section of the discrete-continuous inter-resonance vibrating table
Date
2022-02-22
Journal Title
Journal ISSN
Volume Title
Publisher
Видавництво Львівської політехніки
Lviv Politechnic Publishing House
Lviv Politechnic Publishing House
Abstract
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.
Description
Keywords
inter-resonance vibrating machine, continuous member, elastic plate, the natural frequency of body oscillations, Rayleigh-Ritz method
Citation
Approximate calculation of natural frequencies of oscillations of the plate with variable cross-section of the discrete-continuous inter-resonance vibrating table / Oleksii Lanets, Pavlo Maistruk, Volodymyr Maistruk, Iryna Derevenko // Ukrainian Journal of Mechanical Engineering and Materials Science. — Lviv : Lviv Politechnic Publishing House, 2022. — Vol 8. — No 2. — P. 41–50.