Integral characteristics of free vibration decay in a sandwich beam with a viscoelastic core
UDC
539.3EDN
GZPKHIDOI:
10.31429/vestnik-23-3-19-26Abstract
The decay of free vibrations of a symmetric three-layer beam with a lightweight viscoelastic core is studied under arbitrary initial conditions. The equations of motion are derived from the variational principle with account of the Rayleigh dissipative function incorporating shear and longitudinal mechanisms of internal friction. The solution is constructed by the Bubnov–Galerkin method using the eigenmodes of the corresponding elastic problem. Integral decay characteristics are introduced: relative residual energy, effective logarithmic decrement, and decay time to a prescribed level. A numerical analysis is carried out for a beam with D16T alloy face sheets and a polystyrene foam core. Two types of initial conditions are considered: an initial deflection in the first eigenmode and a concentrated impulse. It is shown that under an impulse the effective decrement at the initial instant significantly exceeds the decrement of the fundamental mode and approaches it after the higher modes decay. For the first eigenmode the decay proceeds uniformly throughout the entire process.
Keywords:
sandwich beam, free vibrations, viscoelastic damping, Bubnov-Galerkin method, effective decrement, residual energy, decay timeFunding information
The study did not have sponsorship.
References
- Леоненко, Д.В., Колебания трехслойного стержня на основании Пастернака. Экологический вестник научных центров Черноморского экономического сотрудничества, 2018, т. 15, № 3, с. 32–38. [Leonenko, D.V., Fluctuations of sandwich beam on a Pasternak's foundation. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2018, vol. 15, no. 3, pp. 32–38. (in Russian)] DOI: 10.31429/vestnik-15-3-32-38 EDN: YABSXJ
- Starovoitov, E.I., Leonenko, D.V., Bending of a sandwich beam by local loads in the temperature field. Izvestiya of Saratov University. Mathematics. Mechanics. Informatics, 2018, vol. 18, no. 1, pp. 69–83. DOI: 10.18500/1816-9791-2018-18-1-69-83
- Леоненко, Д.В., Маркова, М.В., Колебания круговой трехслойной пластины под действием линейной во времени внешней нагрузки. Журнал Белорусского государственного университета. Математика. Информатика, 2023, № 1, с. 49–63. [Leonenko, D.V., Markova, M.V., Oscillations of a circular three-layer plate under eexternal linear in time load. Journal of the Belarusian State University. Mathematics and Informatics, 2023, no. 1, pp. 49–63. (in Russian)] DOI: 10.33581/2520-6508-2023-1-49-63
- Леоненко, Д.В., Резонансные колебания сэндвич-стержня с легким заполнителем. В: Механика. Исследования и инновации: международный сборник научных трудов. Гомель, 2025, вып. 18, с. 97–103. [Leonenko, D.V., Resonant vibrations of a sandwich rod with a lightweight core. In: Mechanics. Research and Innovation: International Collection of Scientific Papers, 2025, iss. 18. (in Russian)]
- Прокудин, О.А., Рабинский, Л.Н., Чан, К.Т., Определение динамических характеристик металлополимерного слоистого стержня. Труды МАИ, 2021, № 119. [Prokudin, O.A., Rabinskiy, L.N., Thang, Q.T., Determination of the Dynamic Characteristics of a metal-polymer laminated rod. Trudy MAI, 2021, no. 119. (in Russian)] DOI: 10.34759/trd-2021-120-06
- Фам, Т.Д., Тарлаковский, Д.В., Нестационарные продольные колебания электромагнитоупругого стержня. Экологический вестник научных центров Черноморского экономического сотрудничества, 2020, т. 17, № 2, с. 57–65. [Pham, T.D., Tarlakovskii, D.V., Non-stationary Longitudinal Vibrationsof an Electromagnetoelastic Rod. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2020, vol. 17, no. 2, pp. 57–65. (in Russian)] DOI: 10.31429/vestnik-17-2-57-65 EDN: QOCJLR
- Шмид, Г., Калинчук, В.В., Белянкова, Т.И., Тосецки, А., Колебания слоисто неоднородной среды под действием движущейся по ее поверхности осциллирующей нагрузки. Экологический вестник научных центров Черноморского экономического сотрудничества, 2004, № 1, с. 60–67. [Schmid, G., Kalinchuk, V.V., Belyankova, T.I., Tosecki, A., Vibrations of a layered inhomogeneous medium under the action of oscillating load moving on its surface. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2004, no. 1, pp. 60–67. (in Russian)] EDN: QQPUEZ
- Саиян, С.Г., Марасанова, А.А., Иванченко, К.Д., Модестов, К.А., Гармонические продольные волны в дискретно-неоднородных вязкоупругих стержнях. Вестник МГСУ, 2026, т. 21, № 2, с. 207–218. [Saiyan, S.G., Marasanova, A.A., Ivanchenko, K.D., Modestov, K.A., Harmonic longitudinal waves in discretely inhomogeneous viscoelastic rods. Vestnik MGSU, 2026, vol. 21, no. 2, pp. 207–218. (in Russian)] DOI: 10.22227/1997-0935.2026.2.207-218
- Рябов, В.М., Ярцев, Б.А., Методы моделирования диссипативных характеристик слоистых композитов. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия, 2024, т. 11, № 3, с. 570–583. [Ryabov, V.M., Yartsev, B.A., Methods for modeling the dissipative characteristics of layered composites. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2024, vol. 11, no. 3, pp. 570–583. (in Russian)] DOI: 10.21638/spbu01.2024.313
- Рябов, В.М., Ярцев, Б.А., Паршина, Л.В., Затухающие колебания неоднородных композитных стержней коробчатого сечения. Вестник Санкт-Петербургского университета. Математика. Механика. Астрономия, 2025, т. 12, № 1, с. 407–418. [Ryabov, V.M., Yartsev, B.A., Parshina, L.V., Damped vibrations of inhomogeneous composite box rods. Vestnik of Saint Petersburg University. Mathematics. Mechanics. Astronomy, 2025, vol. 12, no. 1, pp. 407–418. (in Russian)]
- Friedel, H., Kroll, L., Hufenbach, W., Hanselka, H., Structural-dynamic and vibro-acoustic analysis of fibre-reinforced and sandwich structures. Proceedings of the 32nd International SAMPE Technical Conference, 2000, pp. 443–454.
- Dubenets, V.G., Vibrations of three-layer plates with an allowance for energy dissipation in the material. Strength of Materials, 1970, no. 2, pp. 82–85. DOI: 10.1007/BF01527197
- Kong, S., Zhao, G., Ma, Y., Dong, Y., Yang, Z., Feng, R., A novel three-layer ring springs-based self-centering damper: Development, experiment, and numerical simulation, Engineering Structures, 2026, vol. 353, art. 122231. DOI: 10.1016/j.engstruct.2026.122231
Downloads
Download data is not yet available.
Downloads
Dates
Submitted
August 4, 2026
Accepted
September 23, 2026
Published
September 25, 2026
How to Cite
[1]
Leonenko, D.V., Integral characteristics of free vibration decay in a sandwich beam with a viscoelastic core. Ecological Bulletin of Research Centers of the Black Sea Economic Cooperation, 2026, т. 23, № 3, pp. 19–26. DOI: 10.31429/vestnik-23-3-19-26
License
Copyright (c) 2026 Леоненко Д.В.
This work is licensed under a Creative Commons Attribution 4.0 International License.
