Modelling of Forced Vibrations of Ultrasound Concentrators Based on Ring-Shaped Elastic Element
https://doi.org/10.21122/2227-1031-2025-24-3-234-245
Abstract
The article considers methodology for modelling forced vibrations of ultrasound concentrators based on ring-shaped elastic elements and compound vibratory systems including such concentrators. As a background for modelling we used solution of non-homogeneous differential equation of forced vibrations based on series expansion by eigenfunctions of the corresponding homogeneous problem. As a result we obtained expressions for the gain factor of vibrations amplitude and the input mechanical impedance allowing to study the effect of design parameters on the main operational characteristics of vibratory systems containing ring-shaped concentrators. The obtained numerical results are verified by comparing them to the results of modelling by means of finite element method. It is shown that a compound vibratory system consisting of serially connected bar waveguide and a ring-shaped concentrator enables gain of vibrations amplitude under condition that elements of the system have close values of anti-resonance frequencies. It has been determined that gain of a compound vibratory system can be improved by increasing.
Crossectional area of the bar waveguide and/or specific acoustic impedance of its material, as well as by means of optimal choice of mismatch value between anti-resonant frequencies of the system elements. An explanation is also given of the mechanism of vibrations amplification by means of uniform ring-shaped concentrator based on an analysis of the interaction between plurality of vibration modes excited in concentrator in the case of its near-resonant operation.
About the Authors
D. A. Stepanenko
Belarussian National Technical University
Belarus
Belarus
Minsk, Republic of Belarus
A. N. Kindruk
Belarussian National Technical University
Belarus
Belarus
Minsk, Republic of Belarus
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Review
For citations:
Stepanenko D.A., Kindruk A.N. Modelling of Forced Vibrations of Ultrasound Concentrators Based on Ring-Shaped Elastic Element. Science & Technique. 2025;24(3):234-245. (In Russ.) https://doi.org/10.21122/2227-1031-2025-24-3-234-245
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