Geometrically nonlinear response of axially functionally graded beams subjected to a moving load
Email:
phamthibalien@utc.edu.vn
Từ khóa:
AFG beam, dynamic response, trigonometric shear deformation beam theory, von-Kármán geometric nonlinearity, finite element formula.
Tóm tắt
Understanding the dynamic response of the beam under the actions of a moving load is crucial for practical applications. In this study, nonlinear dynamic characteristics of an axially functionally graded (AFG) beam subjected to a moving load has been performed by using the trigonometric shear deformation beam theory and the von-Kármán geometric nonlinearity. The Voigt model is used to calculate the material properties of the beam. The system of nonlinear differential equation of motion for the beam is derived by using Hamilton’s principle. The finite element formula based on the Lagrange and Hermite interpolation functions is employed to discretize the model and obtain a numerical approximation of the system of differential equation of motion in nonlinear analysis. The Newmark method together with the Newton-Raphson iteration method is adopted to solved these equations. To validate the present work, the results in this paper are compared with those of the existing literature and good agreement is achieved. The results show that the power-law index, velocity and moving load magnitude and aspect ratio play a very important role on the beam’s nonlinear response.Tài liệu tham khảo
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[15]. Q. Zhang, H. Liu, On the dynamic response of porous functionally graded microbeam under moving load, International Journal of Engineering Science, 153 (2020) 103317. https://doi.org/10.1016/j.ijengsci.2020.103317
[16]. M. Şimşek, Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load, Composite Structures, 92 (2010) 2532-2546. https://doi.org/10.1016/j.compstruct.2010.02.008
[17]. H. Lohar, A. Mitra, S. Sahoo, Nonlinear response of axially functionally graded Timoshenko beams on elastic foundation under harmonic excitation, Curved and Layered Structures, 6 (2019) 90-104.
[18]. A. N. T. Vu, D. K. Nguyen, Nonlinear dynamics of two-directional functionally graded beam under a moving load with influence of homogenization scheme, Journal of Vibration Engineering & Technologies, 12 (2024) 171-185. https://doi.org/10.1007/s42417-024-01409-w
[19]. M. Touratier, An efficient standard plate theory, Int J Eng Sci, 29 (1991) 901–16. https://doi.org/10.1016/0020-7225(91)90165-Y
[2]. Y. H. Lin, Vibration analysis of Timoshenko beams traversed by moving loads, Journal of Marine Science and Technology, 2 (1994) 4. https://jmstt.ntou.edu.tw/journal/vol2/iss1/4
[3]. H. A. F. A. Santos, A new finite element formulation for the dynamic analysis of beams under moving loads, Computers & Structures, 298 (2024) 107347. https://doi.org/10.1016/j.compstruc.2024.107347
[4]. A. Mamandi, M. H. Kargarnovin, D. Younesian, Nonlinear dynamics of an inclined beam subjected to a moving load, Nonlinear Dynamics, 60 (2010), 277-293. https://doi.org/10.1007/s11071-009-9595-8
[5]. M. Koizumi, FGM activities in Japan, Compos. Part B Eng, 28 (1997) 1–4. https://doi.org/10.1016/S1359-8368(96)00016-9
[6]. S. M. R. Khalili, A. A. Jafari, S. A. Eftekhari, A mixed Ritz-DQ method for forced vibration of functionally graded beams car rying moving loads, Compos Struct, 92 (2010) 2497–2511. https:// doi. org/ 10. 1016/j. comps truct. 2010. 02. 012
[7]. I. Esen, Dynamic response of a functionally graded Timoshenko beam on two-parameter elastic foundations due to a variable velocity moving mass, Int J Mech Sci, 153 (2019) 21–35. https:// doi. org/ 10. 1016/j. ijmec sci. 2019. 01. 033
[8]. M. Şimşek, T. Kocatürk, Ş. D. Akbaş, Dynamic behavior of an axially functionally graded beam under action of a moving harmonic load, Composite Structures, 94 (2012), 2358-2364. https://doi.org/10.1016/j.compstruct.2012.03.020
[9]. B. S. Gan, T. H. Trinh, T. H. Le, D. K. Nguyen, Dynamic response of non-uniform Timoshenko beams made of axially FGM subjected to multiple moving point loads, Structural Engineering and Mechanics, An Int'l Journal, 53 (2015) 981-995. http://dx.doi.org/10.12989/sem.2015.53.5.981
[10]. Y. Wang, D. Wu, Thermal effect on the dynamic response of axially functionally graded beam subjected to a moving harmonic load, Acta Astronautica, 127 (2016) 171-181. https://doi.org/10.1016/j.actaastro.2016.05.030
[11]. A. Ebrahimi-Mamaghani, H. Sarparast, M. Rezaei, On the vibrations of axially graded Rayleigh beams under a moving load, Applied Mathematical Modelling, 84 (2020) 554-570. https://doi.org/10.1016/j.apm.2020.04.002
[12]. V. T. A. Ninh, N. T. K. Khue, Dynamic finite element modeling of axially functionally graded Timoshenko microbeams under a moving mass, Journal of Science and Technology in Civil Engineering (JSTCE)-HUCE, 17 (2023) 128-139. https://doi.org/10.31814/stce.huce2023-17(3)-10
[13]. D. K. Nguyen, Q. H. Nguyen, T. T. Tran, V. T. Bui, Vibration of bi-dimensional functionally graded Timoshenko beams excited by a moving load, Acta Mechanica, 228 (2017) 141-155. https://doi.org/10.1007/s00707-016-1705-3
[14]. A. A. Abdelrahman, M. Ashry, A. E. Alshorbagy, W. S. Abdallah, On the mechanical behavior of two directional symmetrical functionally graded beams under moving load, International Journal of Mechanics and Materials in Design, 17 (2021) 563-586. https://doi.org/10.1007/s10999-021-09547-9
[15]. Q. Zhang, H. Liu, On the dynamic response of porous functionally graded microbeam under moving load, International Journal of Engineering Science, 153 (2020) 103317. https://doi.org/10.1016/j.ijengsci.2020.103317
[16]. M. Şimşek, Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load, Composite Structures, 92 (2010) 2532-2546. https://doi.org/10.1016/j.compstruct.2010.02.008
[17]. H. Lohar, A. Mitra, S. Sahoo, Nonlinear response of axially functionally graded Timoshenko beams on elastic foundation under harmonic excitation, Curved and Layered Structures, 6 (2019) 90-104.
[18]. A. N. T. Vu, D. K. Nguyen, Nonlinear dynamics of two-directional functionally graded beam under a moving load with influence of homogenization scheme, Journal of Vibration Engineering & Technologies, 12 (2024) 171-185. https://doi.org/10.1007/s42417-024-01409-w
[19]. M. Touratier, An efficient standard plate theory, Int J Eng Sci, 29 (1991) 901–16. https://doi.org/10.1016/0020-7225(91)90165-Y
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27/12/2025
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12/05/2026
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13/05/2026
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15/05/2026
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Kiểu trích dẫn
Pham Thi Ba, L. (1778778000). Geometrically nonlinear response of axially functionally graded beams subjected to a moving load. Tạp Chí Khoa Học Giao Thông Vận Tải, 77(4), 446-458. https://doi.org/10.47869/tcsj.77.4.8
