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
References
1. Astashev V. K., Krupenin V. L. (2016) Nonlinear Dynamics of Ultrasonic Technological Processes. Moscow, Moscow State University of Printing Arts named after Ivan Fedorov. 372 (in Russian).
2. Lugovoi V. P., Lugovoi I. V. (2018) Determination of Dimensional Parameters for Annular Concentrator of Ultrasonic System. Nauka i Tehnika = Science & Technique, 17 (1), 51–55. https://doi.org/10.21122/2227-1031-2018-17-1-51-55 (in Russian).
3. Stepanenko D. A., Emel'yanova A. S., Pleskach M. A., Solodkaya N. V. (2018) Study of the Characteristics of Composite Ring Concentrators of Ultrasonic Vibrations Using the Transfer Matrix Method. Technical Acoustics, (2). Available at: https://ejta.org/archive/articles2018/stepanenko2.pdf (in Russian).
4. Bai F., Wang L., Yang K., He Z., Qi G., Twiefel J. (2020) Experimental Investigation of Peening Cylindrical Workpieces Utilizing a Transducer with Ring Sonotrode. Applied Sciences, 11 (1), 94. https://doi.org/10.3390/app11010094.
5. Lu Z.-Q., Gu D.-H., Ding H., Lacarbonara W., Chen L.-Q. (2020) Nonlinear Vibration Isolation Via a Circular Ring. Mechanical Systems and Signal Processing, 136, 106490. https://doi.org/10.1016/j.ymssp.2019.106490.
6. Greenberg L., Marletta M. (2000) Numerical Methods for Higher Order Sturm–Liouville Problems. Journal of Computational and Applied Mathematics, 125 (1–2), 367–383. https://doi.org/10.1016/s0377-0427(00)00480-5.
7. Korn G., Korn T. (1970) Mathematical Handbook forScientists and Engineers. Moscow, Nauka Publ. 720 (in Russian).
8. Fedotov I., Fedotova T., Shatalov M., Tenkam H. M. (2009) Application of Eigenfunction Orthogonalities to Vibration Problems. Proc. of the World Congress on Engineering. London. Vol. II, 1169–1173. Available at: https://researchspace.csir.co.za/server/api/core/bitstreams/da4c7905-7772-461b-a5be-2a5262ef8822/content.
9. Stepanenko D. A., Bunchuk K. A. (2021) Mathematical Modelling of Vibrations of Non-Uniform Ring-Shaped Ultrasonic Waveguides. Mechanics of Machines, Mechanisms and Materials, 3 (56), 90–96. https://doi.org/10.46864/1995-0470-2021-3-56-90-96 (in Russian).
10. Li L. (1996) Use of Fourier Series in the Analysis of Discontinuous Periodic Structures. Journal of the Optical Society of America A, 13 (9), 1870. https://doi.org/10.1364/josaa.13.001870.
11. Thao N. X., Tuan V. K., Hong N. T. (2007) Integral Transforms of Fourier Cosine and Sine Generalized Convolution Type. International Journal of Mathematics and Mathematical Sciences, 2007, 097250. https://doi.org/10.1155/2007/97250.
12. Hirashima K., Hirano K. (1990) Higher-order theories for free vibration analysis of circular rings. Journal of the Japan Society of Civil Engineers, 1990 (416), 201–204 (in Japanese). https://doi.org/10.2208/jscej.1990.416_201.
13. Heckl M. A. (1961) Compendium of Impedance Formulas. Bolt Beranek and Newman Report No 774. Cambridge. 49. https://doi.org/10.21236/ad0257966.
14. Zeveke G. V., Ionkin P. A., Netushil A. V., Strakhov S. V. (1975) Fundamentals of Circuit Theory. Moscow, Energiya Publ. 752 (in Russian).
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
Views:
13
Email this article 