Finite Element Analysis of a Continuous Sandwich Beam resting on Elastic Support and Subjected to Two Degree of Freedom Sprung Vehicles
Received: 3 November 2022 | Revised: 4 December 2022 | Accepted: 12 December 2022 | Online: 26 March 2023
Corresponding author: Nguyen Van Thuan
Abstract
This paper has developed a Finite Element Method (FEM) to calculate the dynamic response of a continuous sandwich beam resting on elastic support subjected to moving vehicles. The equation of motion is derived using the classical beam theory and FEM. The vehicle model is a two Degree of Freedom (2DOF) system that moves with a constant velocity. The governing equation of motion is integrated by applying the Wilson-θ time integration method to obtain the dynamic response in each time step. Numerical examples investigate the displacement of the sandwich beam with various values of the structure and vehicle velocity. The effects of the stiffness of elastic support and the vehicle velocity on displacement are studied.
Keywords:
FEM, forced vibration, continuous beam, elastic supportDownloads
References
P. C. Nguyen, D. D. Pham, T. T. Tran, and T. Nghia-Nguyen, "Modified Numerical Modeling of Axially Loaded Concrete-Filled Steel Circular-Tube Columns," Engineering, Technology & Applied Science Research, vol. 11, no. 3, pp. 7094–7099, Jun. 2021. DOI: https://doi.org/10.48084/etasr.4157
D. T. Hang, X. T. Nguyen, and D. N. Tien, "Stochastic Buckling Analysis of Non-Uniform Columns Using Stochastic Finite Elements with Discretization Random Field by the Point Method," Engineering, Technology & Applied Science Research, vol. 12, no. 2, pp. 8458–8462, Apr. 2022. DOI: https://doi.org/10.48084/etasr.4819
P. H. V. Nguyen and P. C. Nguyen, "Effects of Shaft Grouting on the Bearing Behavior of Barrette Piles: A Case Study in Ho Chi Minh City," Engineering, Technology & Applied Science Research, vol. 11, no. 5, pp. 7653–7657, Oct. 2021. DOI: https://doi.org/10.48084/etasr.4389
P. B. Thang and L. V. Anh, "Structural analysis of steel-concrete composite beam bridges utilizing the shear connection model," Transport and Communications Science Journal, vol. 72, no. 7, pp. 811–823, 2021. DOI: https://doi.org/10.47869/tcsj.72.7.4
D. X. Quy and V. T. Nga, "Static analysis of beam resting on elastic foundation by anisotropic beam-foundation element taking into account non-contact between beam and foundation," Transport and Communications Science Journal, vol. 72, no. 5, pp. 552–564, 2021.
P.-C. Nguyen, T. N. Van, and H. T. Duy, "Stochastic Free Vibration Analysis of Beam on Elastic Foundation with the Random Field of Young’s Modulus Using Finite Element Method and Monte Carlo Simulation," in 6th International Conference on Geotechnics, Civil Engineering and Structures, Ha Long, Vietnam, Oct. 2021, pp. 499–506. DOI: https://doi.org/10.1007/978-981-16-7160-9_50
G. Qiao and S. Rahmatalla, "Dynamics of Euler-Bernoulli beams with unknown viscoelastic boundary conditions under a moving load," Journal of Sound and Vibration, vol. 491, Jan. 2021, Art. no. 115771. DOI: https://doi.org/10.1016/j.jsv.2020.115771
P. Hoa and P.-C. Nguyen, "Effects of size-dependence on static and free vibration of FGP nanobeams using finite element method based on nonlocal strain gradient theory," Steel and Composite Structures, vol. 45, pp. 331–348, Nov. 2022.
P. C. Nguyen, "Nonlinear Inelastic Earthquake Analysis of 2D Steel Frames," Engineering, Technology & Applied Science Research, vol. 10, no. 6, pp. 6393–6398, Dec. 2020. DOI: https://doi.org/10.48084/etasr.3855
M. Usarov, G. Mamatisaev, and G. Ayubov, "Forced vibrations of a box element of a multi-story building under dynamic impact," Magazine of Civil Engineering, vol. 114, no. 6, pp. 11406–11406, 2022.
J. G. R. Iniguez, M. L. Daza-Torres, A. P. Gonzalez, and A. Cros, "Natural frequency of a heavy flexible plate: power law evolution as a function of length," Latin American Journal of Solids and Structures, vol. 18, no. 5, Jun. 2021, Art. no. e377. DOI: https://doi.org/10.1590/1679-78256479
A. P. Yankovskii, "Analysis of Thermal Response in Reinforced Plates under a Dynamic Explosion-Type Loading," Mechanics of Composite Materials, vol. 57, no. 4, pp. 439–448, Sep. 2021. DOI: https://doi.org/10.1007/s11029-021-09967-w
L. Zhang et al., "High-hardness polyurea coated steel plates subjected to combined loadings of shock wave and fragments.," Latin American Journal of Solids and Structures, vol. 19, no. 2, Feb. 2022, Art. no. e433. DOI: https://doi.org/10.1590/1679-78256882
A. Dasdemir, "A Modal Analysis of Forced Vibration of a Piezoelectric Plate with Initial Stress by the Finite-Element Simulation," Mechanics of Composite Materials, vol. 58, no. 1, pp. 69–80, Mar. 2022. DOI: https://doi.org/10.1007/s11029-022-10012-7
Q.-H. Pham and P.-C. Nguyen, "Dynamic stability analysis of porous functionally graded microplates using a refined isogeometric approach," Composite Structures, vol. 284, Mar. 2022, Art. no. 115086. DOI: https://doi.org/10.1016/j.compstruct.2021.115086
V. Karpilovsky, "Finite elements for the analysis of reissne-rmindlin plates with joint interpolation of displacements and rotations," International Journal for Computational Civil and Structural Engineering, vol. 17, no. 3, pp. 48–62, Sep. 2021. DOI: https://doi.org/10.22337/2587-9618-2021-17-3-48-62
Q.-H. Pham, P.-C. Nguyen, and T. Thanh Tran, "Dynamic response of porous functionally graded sandwich nanoplates using nonlocal higher-order isogeometric analysis," Composite Structures, vol. 290, Jun. 2022, Art. no. 115565. DOI: https://doi.org/10.1016/j.compstruct.2022.115565
B. Uymaz, "Buckling Characteristics of FGM Plates Subjected to Linearly Varying In-Plane Loads," Mechanics of Composite Materials, vol. 57, no. 1, pp. 69–80, Mar. 2021. DOI: https://doi.org/10.1007/s11029-021-09934-5
H. D. Ta and P.-C. Nguyen, "Perturbation based stochastic isogeometric analysis for bending of functionally graded plates with the randomness of elastic modulus," Latin American Journal of Solids and Structures, vol. 17, no. 7, Sep. 2020, Art. no. e306. DOI: https://doi.org/10.1590/1679-78256066
N. V. Thuan and T. D. Hien, "Stochastic Perturbation-Based Finite Element for Free Vibration of Functionally Graded Beams with an Uncertain Elastic Modulus," Mechanics of Composite Materials, vol. 56, no. 4, pp. 485–496, Sep. 2020. DOI: https://doi.org/10.1007/s11029-020-09897-z
D. K. Nguyen, T. T. Tran, V. N. Pham, and N. A. T. Le, "Dynamic analysis of an inclined sandwich beam with bidirectional functionally graded face sheets under a moving mass," European Journal of Mechanics - A/Solids, vol. 88, Jul. 2021, Art. no. 104276. DOI: https://doi.org/10.1016/j.euromechsol.2021.104276
G. Qiao and S. Rahmatalla, "Dynamics of interaction between an Euler-Bernoulli beam and a moving damped sprung mass: Effect of beam surface roughness," Structures, vol. 32, pp. 2247–2265, Aug. 2021. DOI: https://doi.org/10.1016/j.istruc.2021.04.020
Q.-H. Pham, V. K. Tran, and P.-C. Nguyen, "Hygro-thermal vibration of bidirectional functionally graded porous curved beams on variable elastic foundation using generalized finite element method," Case Studies in Thermal Engineering, vol. 40, Dec. 2022, Art. no. 102478. DOI: https://doi.org/10.1016/j.csite.2022.102478
A. W. de Q. R. Reis, R. B. Burgos, and M. F. F. de Oliveira, "Nonlinear Dynamic Analysis of Plates Subjected to Explosive Loads," Latin American Journal of Solids and Structures, vol. 19, no. 1, Jan. 2022, Art. no. e422. DOI: https://doi.org/10.1590/1679-78256706
Q.-H. Pham, P.-C. Nguyen, V.-K. Tran, and T. Nguyen-Thoi, "Finite element analysis for functionally graded porous nano-plates resting on elastic foundation," Steel and Composite Structures, vol. 41, no. 2, pp. 149–166, 2021.
M. V. Shitikova and A. I. Krusser, "Force driven vibrations of nonlinear plates on a viscoelastic winkler foundation under the harmonic moving load," International Journal for Computational Civil and Structural Engineering, vol. 17, no. 4, pp. 161–180, Dec. 2021. DOI: https://doi.org/10.22337/2587-9618-2021-17-4-161-180
T. D. Hien and N. N. Lam, "Vibration of functionally graded plate resting on viscoelastic elastic foundation subjected to moving loads," IOP Conference Series: Earth and Environmental Science, vol. 143, no. 1, Dec. 2018, Art. no. 012024. DOI: https://doi.org/10.1088/1755-1315/143/1/012024
N. T. Nguyen, H. D. Ta, T. N. Van, and T. N. Dao, "Stochastic finite element analysis of the free vibration of non-uniform beams with uncertain material," Journal of Materials and Engineering Structures, vol. 9, no. 1, pp. 29–37, Apr. 2022.
T. D. Hien, N. D. Hung, N. T. Kien, and H. C. Noh, "The variability of dynamic responses of beams resting on elastic foundation subjected to vehicle with random system parameters," Applied Mathematical Modelling, vol. 67, pp. 676–687, Mar. 2019. DOI: https://doi.org/10.1016/j.apm.2018.11.018
G. Muscolino and A. Palmeri, "Response of beams resting on viscoelastically damped foundation to moving oscillators," International Journal of Solids and Structures, vol. 44, no. 5, pp. 1317–1336, Mar. 2007. DOI: https://doi.org/10.1016/j.ijsolstr.2006.06.013
Y. Karmi, Y. Khadri, S. Tekili, A. Daouadji, and E. M. Daya, "Dynamic Analysis of Composite Sandwich Beams with a Frequency-Dependent Viscoelastic Core under the Action of a Moving Load," Mechanics of Composite Materials, vol. 56, no. 6, pp. 755–768, Jan. 2021. DOI: https://doi.org/10.1007/s11029-021-09921-w
L. Li, B. Han, Q.-C. Zhang, Z.-Y. Zhao, and T. J. Lu, "Dynamic response of clamped sandwich beams: analytical modeling," Theoretical and Applied Mechanics Letters, vol. 9, no. 6, pp. 391–396, Nov. 2019. DOI: https://doi.org/10.1016/j.taml.2019.06.002
Z. Dimitrovova, "Dynamic interaction and instability of two moving proximate masses on a beam on a Pasternak viscoelastic foundation," Applied Mathematical Modelling, vol. 100, pp. 192–217, Dec. 2021. DOI: https://doi.org/10.1016/j.apm.2021.07.022
R. Chawla and V. Pakrashi, "Dynamic responses of a damaged double Euler–Bernoulli beam traversed by a ‘phantom’ vehicle," Structural Control and Health Monitoring, vol. 29, no. 5, 2022, Art. no. e2933. DOI: https://doi.org/10.1002/stc.2933
H. Ding, Y. Yang, L.-Q. Chen, and S.-P. Yang, "Vibration of vehicle–pavement coupled system based on a Timoshenko beam on a nonlinear foundation," Journal of Sound and Vibration, vol. 333, no. 24, pp. 6623–6636, Dec. 2014. DOI: https://doi.org/10.1016/j.jsv.2014.07.016
J. L. Humar and A. M. Kashif, "Dynamic response of bridges under travelling loads," Canadian Journal of Civil Engineering, vol. 20, no. 2, pp. 287–298, Apr. 1993. DOI: https://doi.org/10.1139/l93-033
P. K. Chatterjee and T. K. Datta, "Dynamic analysis of arch bridges under travelling loads," International Journal of Solids and Structures, vol. 32, no. 11, pp. 1585–1594, Jun. 1995. DOI: https://doi.org/10.1016/0020-7683(94)00193-Z
Y.-M. Wang, "The dynamic analysis of a beam-mass system due to the occurrence of two-component parametric resonance," Journal of Sound and Vibration, vol. 258, no. 5, pp. 951–967, Dec. 2002. DOI: https://doi.org/10.1006/jsvi.2002.5183
L. Jing, Z. Wang, J. Ning, and L. Zhao, "The mechanical response of metallic sandwich beams under foam projectile impact loading," Latin American Journal of Solids and Structures, vol. 8, pp. 107–120, 2011. DOI: https://doi.org/10.1590/S1679-78252011000100006
J. Reddy, An Introduction to the Finite Element Method, 3rd ed. New York, NY, USA: McGraw-Hill Education, 2005.
Downloads
How to Cite
License
Copyright (c) 2022 Ta Duy Hien, Nguyen Duy Hung, Nguyen Trong Hiep , Giap Van Tan , Nguyen Van Thuan
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.