Dynamic analysis of reinforced concrete plate resting on elastic foundation using state space method and refined plate theory

Authors

  • Nguyen Trong Hiep University of Transport and Communications

DOI:

https://doi.org/10.21776/ub.civense.2023.00601.10

Keywords:

plate, elastic foundation, dynamic analysis, pavement, airport

Abstract

This paper studies the dynamic response of rectangular reinforced concrete plates on an elastic foundation by state space method. The system of differential equations of vibration of the plate is developed by using Hamilton's principle. With a single-link rectangular plate, the displacements are represented through a double trigonometric series. Use the state space method to find the plate vibrational responses. The calculation examples are performed to calculate the displacement and stress of the plate with different structural parameters, thereby evaluating the influence of these parameters.

References

P. L. Pasternak, "On a new method of analysis of an elastic foundation by means of two foundation constants," Cosudarstrennoe Izdatelstvo Literaturi po Stroitelstvu i Arkhitekture, 1954.

M. R. Madhav, H. B. Poorooshasb, "Modified pasternak model for reinforced soil," Mathematical and Computer Modeling, 12 (12): p. 1505-1509, 1989.

A. A. Khdeir, J. N. Reddy, "Exact-Solutions for the Transient-Response of Symmetric Cross-Ply Laminates Using a Higher-Order Plate-Theory," Composites Science and Technology, 34 (3): p. 205-224, 1989.

H. S. Shen, J. J. Zheng, and X. L. Huang, "Dynamic response of shear deformable laminated plates under thermomechanical loading and resting on elastic foundations," Composite Structures, 60 (1): p. 57-66, 2003.

U. S. Gupta, and A. H. Ansari, "Forced axi-symmetric response of polar orthotropic linearly tapered circular plates," Journal of Sound and Vibration, 236 (4): p. 623-636, 2000.

R. S. Weiner, "Transient Motion of Circular Elastic Plates Subjected to Impulsive and Moving Loads," Bell System Technical Journal, 44 (10): p. 2409-2431, 1965.

T. D. Hien, and B.T. Quang, "Analysis of isotropic rectangular plate resting on non-uniform elastic foundation using Ritz approach," Materials Today, Proceedings, 2019.

Phung-Van, P., et al., "A cell-based smoothed discrete shear gap method (CS-FEM-DSG3) using layerwise deformation theory for dynamic response of composite plates resting on viscoelastic foundation," Computer Methods in Applied Mechanics and Engineering, 272 (Supplement C): p. 138-159, 2014.

N. T. Trung, et al., "Dynamic analysis of Mindlin plates on viscoelastic foundations under a moving vehicle by CS-MIN3 based on C-type higher-order shear deformation theory," Vietnam Journal of Mechanics, 36 (1), 2014.

N. V. Loi, and T. M. Tu, "Vibration analysis of cross-ply laminated composite plates using new eight-unknown higher order shear deformation theory," in National Scientific Conference on Composite Materials and Structures, Mechanics, Technology and Applications Application 2016: Nha Trang University, Nha Trang City, Vietnam, 2016.

N. T. Dung, and D. S. Lam, "Calculation of plate structures made of materials with variable mechanical properties fgm taking into account the effect of temperature by finite element method," Science and Technology of Construction, 3, 2014.

H. D. Ta, and H. C. Noh, "Analytical solution for the dynamic response of functionally graded rectangular plates resting on elastic foundation using a refined plate theory," Applied Mathematical Modelling, 39(20), p. 6243-6257, 2015.

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

M. R. Taheri, M. M. Zaman, and A. Alvappillai, "Dynamic response of concrete pavements to moving aircraft," Applied Mathematical Modeling, 14 (11): p. 562-575, 1990.

T. Xiao, et al., "Dynamic Response Analysis of Cement Concrete Pavement under Different Vehicle Speeds," Pavements and Materials: Recent Advances in Design, Testing and Construction, 2012.

R. P. Shimpi, and H. G. Patel, "A two variable refined plate theory for orthotropic plate analysis," International Journal of Solids and Structures, 43 (22–23): p. 6783-6799, 2006.

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Published

2023-04-30

How to Cite

[1]
N. Trong Hiep, “Dynamic analysis of reinforced concrete plate resting on elastic foundation using state space method and refined plate theory”, CIVENSE, vol. 6, no. 1, pp. 84–89, Apr. 2023.

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Section

Articles