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JOURNALS // Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika // Archive

Izv. Vyssh. Uchebn. Zaved. Mat., 2025 Number 5, Pages 68–76 (Mi ivm10090)

On the modeling of vibrations of deformable elements of apparatus structures under vibration disturbing loads

I. I. Safarova, M. Kh. Teshaevb, Sh. I. Juraevc

a Tashkent Institute of Chemical Technology, 36 Navoi str., Tashkent, 100011 Republic of Uzbekistan
b Bukhara Branch of the Institute of Mathematics named after Romanovsky at the Academy of Science of the Republic of Uzbekistan, 11 M. Ikbol str., Bukhara, 200100 Republic of Uzbekistan
c Bukhara State University, 11 M. Ikbol str., Bukhara, 200100 Republic of Uzbekistan

Abstract: The task of reducing the level of vibration of radio-electronic devices (REA) is an urgent task in mechanical engineering of aircraft industry. The purpose of the study is to investigate the vibrations of plate-like elements with attached masses under the influence of vibration loads. All deformable elements are viscoelastic. The viscoelastic properties obey the hereditary Boltzmann-Volterra integral relation. Linear oscillations of the considered mechanical system are investigated. For reduction of impulse perturbations of a radio-electronic unit with attached masses, a method and an algorithm for solving the problem are developed. The method of complex amplitudes, the methods of mathematical physics equations, the Gauss method, the Mueller method and the Godunov orthogonal run method were used in developing a method for solving the problem. An algorithm for determining the resonance frequency and amplitude of displacements of the considered mechanical system was proposed. Application of the proposed mathematical model taking into account viscous properties of the elements allows to reduce the total impulse loads of the REU up to 25%. It is established that the use of rubber shock absorbers reduces the amplitudes of vibrations of the equipment up to 30%. It is also established that the use of dissipative and inhomogeneous design allows maximal reduction (up to 40–50%) of resonant amplitudes of REU in low-frequency ranges.

Keywords: vibration, impulse loading, viscoelastic property, deformable element, vibration load.

UDC: 517.984

Received: 01.03.2024
Revised: 01.03.2024
Accepted: 20.03.2024

DOI: 10.26907/0021-3446-2025-5-68-76



© Steklov Math. Inst. of RAS, 2026