Finite Element Analysis for the Free Vibration of a Rigid Pavement resting on a Non-uniform Elastic Foundation

Authors

  • Bui Tuan Anh University of Transport and Communications, Vietnam
  • Nguyen Trong Hiep University of Transport and Communications, Vietnam
  • Le Vinh An University of Transport and Communications, Vietnam
  • Nguyen Van Lap University of Transport and Communications, Vietnam
Volume: 14 | Issue: 1 | Pages: 12452-12456 | February 2024 | https://doi.org/10.48084/etasr.6039

Abstract

This paper presents a finite element analysis of the free vibration behavior of rigid pavements resting on non-uniform foundations. The rigid pavement was modeled using the Mindlin plate theory, while the supporting soil medium was approximated by a Winkler model with non-uniform stiffness. A finite element formulation was established to govern the equation of free vibration for rigid pavements. Subsequently, a computer program was developed based on the proposed algorithm, enabling the determination of natural frequencies and mode shapes. The accuracy of the proposed method was verified by comparing numerical examples of free vibration with analytical results. These numerical examples also demonstrate the significant influence of the foundation stiffness on natural frequencies and mode shapes.

Keywords:

rigid pavement, FEM, free vibration, nonuniform foundation

Downloads

Download data is not yet available.

References

N. P. Sharifi, S. Chen, Z. You, T. Van Dam, and C. Gilbertson, "A review on the best practices in concrete pavement design and materials in wet-freeze climates similar to Michigan," Journal of Traffic and Transportation Engineering (English Edition), vol. 6, no. 3, pp. 245–255, Jun. 2019.

T. Yan, S. Kitipornchai, J. Yang, and X. Q. He, "Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load," Composite Structures, vol. 93, no. 11, pp. 2992–3001, Oct. 2011.

Q. Đ. Xuân and N. V. Thị, "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.

T. D. Hien, N. D. Hung, N. T. Hiep, G. V. Tan, and N. V. Thuan, "Finite Element Analysis of a Continuous Sandwich Beam resting on Elastic Support and Subjected to Two Degree of Freedom Sprung Vehicles," Engineering, Technology & Applied Science Research, vol. 13, no. 2, pp. 10310–10315, Apr. 2023.

T. D. Hien and B. T. Quang, "Analysis of isotropic rectangular plate resting on non-uniform elastic foundation using Ritz approach," Materials Today: Proceedings, vol. 19, pp. 158–160, Jan. 2019.

V. A. Le, M. P. Pham, and T. A. Bui, "Stability of Cracked Plates with Nonlinearly Variable Thickness Resting on Elastic Foundations," Journal of Materials and Engineering Structures « JMES », vol. 9, no. 4, pp. 641–651, Dec. 2022.

B. K. Eshmatov, R. A. Abdikarimov, M. Amabili, and N. I. Vatin, "Nonlinear vibrations and dynamic stability of viscoelastic anisotropic fiber reinforced plates," Magazine of Civil Engineering, vol. 118, no. 2, 2023, Art. no. 11811.

M. Shitikova and A. 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.

T. D. Hien and N. N. Lam, "Vibration of functionally graded plate resting on viscoelastic elastic foundation subjected to moving loads," in 2nd International Conference on Sustainable Development in Civil, Urban and Transportation Engineering (CUTE 2018), Ho Chi Minh City, Vietnam, Apr. 2018.

D. T. Thuy, L. N. Ngoc, D. N. Tien, and H. V. Thanh, "An Analytical Solution for the Dynamics of a Functionally Graded Plate resting on Viscoelastic Foundation," Engineering, Technology & Applied Science Research, vol. 13, no. 1, pp. 9926–9931, Feb. 2023.

T. C. Yu, G. J. Nie, Z. Zhong, F. Y. Chu, and X. J. Cao, "Analytical Solution of the Bending Problem for Rectangular Orthotropic Plates with a Variable in-Plane Stiffness," Mechanics of Composite Materials, vol. 57, no. 1, pp. 115–124, Mar. 2021.

T. Yury, "Arbitrary Quadrangular Finite Element for Plates with Shear Deformations," Magazine of Civil Engineering, no. 7 (107), 2021, Art. no. 10707.

P.-C. Nguyen, Q. H. Pham, T. T. Tran, and T. Nguyen-Thoi, "Effects of partially supported elastic foundation on free vibration of FGP plates using ES-MITC3 elements," Ain Shams Engineering Journal, vol. 13, no. 3, May 2022, Art. no. 101615.

V. Karpilovsky, "Finite Elements for the Analysis of Reissne-Rmindlin Plates with Joint Interpolation of Displacements and Rotations (JIDR)," International Journal for Computational Civil and Structural Engineering, vol. 17, no. 3, pp. 48–62, Sep. 2021.

Đ. Đ. Hồng, T. Đ. Văn, and P. P. Minh, "Buckling analysis of variable thickness cracked nanoplates considerting the flexoelectric effect," Transport and Communications Science Journal, vol. 73, no. 5, pp. 470–485, 2022.

N. T. Hiep, D. S. Dan, N. D. Diem, and D. N. Tien, "NURBS-based Isogeometric Analysis and Refined Plate Theory Application on a Functionally Graded Plate Subjected to Random Loads," Engineering, Technology & Applied Science Research, vol. 13, no. 2, pp. 10243–10248, Apr. 2023.

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, Sep. 2020, Art. no. e306.

N. T. Hiep, "Dynamic analysis of reinforced concrete plate resting on elastic foundation using state space method and refined plate theory," Civil and Environmental Science Journal (CIVENSE), vol. 6, no. 1, pp. 84–89, Apr. 2023.

E. Bahmyari and A. Rahbar-Ranji, "Free vibration analysis of orthotropic plates with variable thickness resting on non-uniform elastic foundation by element free Galerkin method," Journal of Mechanical Science and Technology, vol. 26, no. 9, pp. 2685–2694, Sep. 2012.

J. Cai, L. N. Y. Wong, and H. W. Yan, "Dynamic Response of Airport Concrete Pavement to Impact Loading," Advanced Materials Research, vol. 594–597, pp. 1395–1401, 2012.

X. P. Shi, S. A. Tan, and T. F. Fwa, "Rectangular Thick Plate with Free Edges on Pasternak Foundation," Journal of Engineering Mechanics, vol. 120, no. 5, pp. 971–988, May 1994.

J. R. Roesler and L. Khazanovich, "Finite-Element Analysis of Portland Cement Concrete Pavements with Cracks," Transportation Research Record, vol. 1568, no. 1, pp. 1–9, Jan. 1997.

V. A. Patil, V. A. Sawant, and K. Deb, "3D Finite-Element Dynamic Analysis of Rigid Pavement Using Infinite Elements," International Journal of Geomechanics, vol. 13, no. 5, pp. 533–544, Oct. 2013.

A. J. M. Ferreira and N. Fantuzzi, MATLAB Codes for Finite Element Analysis: Solids and Structures, vol. 157. Cham, Switzerland: Springer International Publishing, 2020.

Introduction to the finite element method. New York, NY, USA: McGraw-Hill Education, 2019.

J. N. Reddy, Theory and Analysis of Elastic Plates and Shells. Boca Raton, FL, USA: CRC Press, 2006.

A. W. Leissa, Vibration of Plates. Published for the Acoustical Society of America through the American Institute of Physics, 1993.

Downloads

How to Cite

[1]
Anh, B.T., Hiep, N.T., Vinh An, L. and Lap, N.V. 2024. Finite Element Analysis for the Free Vibration of a Rigid Pavement resting on a Non-uniform Elastic Foundation. Engineering, Technology & Applied Science Research. 14, 1 (Feb. 2024), 12452–12456. DOI:https://doi.org/10.48084/etasr.6039.

Metrics

Abstract Views: 942
PDF Downloads: 836

Metrics Information

Most read articles by the same author(s)