Tasodifiy qo‘zg‘alishlarda o‘yiq plastinkaning harakat differensial tenglamasini aniqlash masalasi
This paper investigates the problem of deriving the differential equation of motion for a perforated plate
with hysteretic elastic-dissipative characteristics subjected to random excitations. The dissipative properties of
the plate material are described based on the Pisarenko-Boginich hypothesis. A rectangular plate containing a
rectangular cutout is considered. It is assumed that the sides of the cutout are parallel to the sides of the plate.
Furthermore, the cutout may be located arbitrarily within the plane of the plate. Based on this geometrical
and physical model, the equation of motion of the plate is derived. The proposed model takes into account
both random external excitations and the internal dissipative properties of the material. The obtained equation
provides a theoretical foundation for studying the dynamics of elastic-dissipative systems
1. K. D. Mali and P. M. Singru, “Determination of the Fundamental Frequency of Perforated Rectangular
Plates: Concentrated Negative Mass Approach for the Perforation,” Advances in Acoustics and Vibration,
vol. 2013, Art. no. 972409, pp. 1–6, 2013. doi: 10.1155/2013/972409.
2. K. Ghonasgi, K. Bakal, and K. D. Mali, “A Parametric Study on Free Vibration of Multi-Perforated
Rectangular Plates,” Procedia Engineering, vol. 144, pp. 60–67, 2016. doi: 10.1016/j.proeng.2016.05.007.
3. O. R. Barry and E. Y. Tanbour, “Resonant Frequencies of Perforated Plates with Rectangular Slots,”
Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science,
vol. 232, no. 7, pp. 1218–1230, 2018. doi: 10.1177/0954406216683974.
4. Junfeng Liu, Jingjun Lou, Kai Chai, Qingchao Yang, Jiawen Chu, “Vibration Analysis of Internally
Perforated Annular Plate with Discontinuous Boundary Conditions,” International Journal of Structural
Stability and Dynamics, 2023, 24(19). DOI: 10.1142/S0219455424502183.
5. Serhii Kharchenko, Sylwester Samborski, Farida Kharchenko, Andrzej Mitura, Jakub Pa’snik, Izabela
Korzec, “Identification of the Natural Frequencies of Oscillations of Perforated Vibrosurfaces with Holes
of Complex Geometry,” Materials, 2023, 16, 5735. doi: 10.3390/ma16175735.
6. Ying Meng, Xiaoye Mao, Hu Ding, Liqun Chen, “Nonlinear Vibrations of a Composite Circular Plate with
a Rigid Body,” Applied Mathematics and Mechanics, 44(6), 857–876, 2023. doi: 10.1007/s10483-023-3005-8.
7. Bastian Saez, Viviana Meruane, Ruben Fernandez, Erick I. Saavedra Flores, “Numerical Optimization and
Experimental Validation of Finite Perforated Cellular Panels for Vibration Reduction,” Materials, 2025,
18(24), 5620. doi: 10.3390/ma18245620.
8. Kaiyuan Tian, YilongWang, Bo Fang, Dengqing Cao, Kaiping Yu, Xutao Mei, “A Novel Unified Dynamical
Modeling of Perforated Plates Based on Negative Mass Equivalence,” Mechanical Systems and Signal
Processing, 2025. doi: 10.1016/j.ymssp.2025.112723.
9. Kyeong-Hoon Jeong, Myung-Jo Jhung, “Free Vibration Analysis of Partially Perforated Circular Plates,”
Procedia Engineering (X International Conference on Structural Dynamics, EURODYN 2017). doi:
10.1016/j.proeng.2017.09.230.
10. M. A. Ðûæêîâ, Ë. Ì. ßêîâåíêî, Â. Á. Äóñìàòîâ, “Íåëèíåéíûå çàäà÷è äèíàìèêè âèáðîçàùèòíûõ
ñèñòåì.” Ïàâëîâñêèé-Ê.: Òåõíèêà, 1997. 204 ñ.
11. S. P. Timoshenko and S. Woinowsky-Krieger, Theory of Plates and Shells, 2nd ed., New York, NY, USA:
McGraw–Hill, 1959.
Copyright (c) 2025 «ACTA NUUz»
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
.jpg)
1.png)
