Free and forced vibrations of structurally inhomogeneous rod mechanical systems

Ismoil  Safarov; Muhsin  Teshaev; Matlab  Ishmamatov; Nuriddin  Esanov; Azimxan  Bayaly; Sharif  Axmedov; Shavkat Almuratov

doi:10.59400/sv3993

Free and forced vibrations of structurally inhomogeneous rod mechanical systems

Ismoil Safarov
Math Department, Tashkent Chemical-Technological Institute, Tashkent 100011, Uzbekistan
Muhsin Teshaev
Bukhara Branch of Institute of Mathematics named after V.I. Romanivskii, Academy of Sciences of the Republic of Uzbekistan (AS R Uz),Bukhara 200100, Uzbekistan
Matlab Ishmamatov
Math Department, Navoi State University of Mining and Technologies, Navoi 210100, Uzbekistan
Nuriddin Esanov
Department of Pedagogy and Psychology, Asia International University, Bukhara 200100, Uzbekistan
Azimxan Bayaly
Computer Engineering Department, International Kazakh-Turkish University named after Yasavi, Turkestan 161200, Kazakhstan
Sharif Axmedov
Hydrotechnical Facilities and Pumping Stations Department, Bukhara State Technical University, Bukhara 200100, Uzbekistan
Shavkat Almuratov
Mathematics and Natural Sciences Department, Renessans University, Tashkent 100071, Uzbekistan

Article ID: 3993

Keywords: natural frequency; steady-state oscillations; oscillation form; dissipative properties; forced oscillations; viscoelastic material

Abstract

The paper investigates free and forced vibrations of structurally inhomogeneous viscoelastic rod mechanical systems. A mechanical system is considered in which the rheological properties of the deformable elements differ significantly: some elements are elastic, while others are viscoelastic with different hereditary functions. Massive deformable elements have finite volumes, whereas massless elements have finite or negligibly small volumes. The deformable elements of the system are made of viscoelastic materials, such as polymers and polymer-based composites, whose physical properties are described by linear Boltzmann–Volterra hereditary constitutive relations with integral difference kernels. The main objective of the work is to study the dissipative properties of such structurally inhomogeneous rod mechanical systems. Moreover, in free oscillations of the system, the manifestation of dissipation reduces to the attenuation of oscillations, the attenuation rate quantitatively assesses the dissipative properties of the system; in steady-state forced oscillations, the dissipative properties are most pronounced in resonant modes and lead to finite values of resonant amplitudes. The natural frequencies and forms of oscillations are determined from the condition that the determinant of the system, calculated by the Müller-Gauss method, is equal to zero. For the considered mechanical system, the fundamental possibility of significantly intensifying dissipative processes in dynamical systems and reducing the resonant amplitudes of principal oscillations due to the convergence of corresponding natural frequencies is shown.

Published

2026-04-20

How to Cite

Safarov, I., Teshaev, M., Ishmamatov, M., Esanov, N., Bayaly, A., Axmedov, S., & Almuratov, S. (2026). Free and forced vibrations of structurally inhomogeneous rod mechanical systems . Sound & Vibration, 60(2). https://doi.org/10.59400/sv3993

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Vol. 60 No. 2 (2026)

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Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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