IJCMP | Dynamic behavior of Moving distributed Masses of Orthotropic Rectangular Plate with Clamped-Clamped Boundary conditions Resting on a Constant Elastic Bi-Parametric Foundation

Indexing and Abstracting

Dynamic behavior of Moving distributed Masses of Orthotropic Rectangular Plate with Clamped-Clamped Boundary conditions Resting on a Constant Elastic Bi-Parametric Foundation

A.S Adeoye , T.O Awodola

International Journal of Chemistry, Mathematics And Physics(IJCMP), Vol-4,Issue-4, July - August 2020, Pages 71-91 , 10.22161/ijcmp.4.4.2

Download | Downloads : 6 | Total View : 1191

Abstract:

This work will investigate the behaviors of Moving distributed masses of orthotropic rectangular plates resting on bi-parametric elastic foundation with clamped-clamped end conditions. The governing equation is a fourth order partial differential equation with variable and singular co-efficients. The solutions to the problem will be obtained by transforming the partial differential equation for the problem to a set of coupled second order ordinary differential equations using the technique of Shadnam et al[18] which shall then be simplified using modified asymptotic method of Struble. The closed form solution will be analyzed, resonance condition shall be obtained and the result will be presented in plotted curves for both cases of moving distributed mass and moving distributed force.

Keywords:

Bi-parametric foundation,orthotropic, foundation modulus, critical speed, resonance, modified frequency.

References:

[1] Euler L. (1766): De Vibrtorio Tympanorum, Novi Comm. Acad. Petropolitanae, t.10, pp 243 - 260 (1766) 1767
[2] Chladni E.F.F (1802): Die Akustik, Leipzig, 1802
[3] Bernoulli J. (1789): Essai Theoretique Sur Les Vibrations Des Plaques Elastiques, Rectangulaires Et Litres, Nova Acta Acad. Sc. Petropolitanae 1789, t.5, pp 197 - 219.
[4] Germain S. (1826): Remarques Sur La Nature Les Bornes et Lâ€™etendue de la Question des Surfaces Elastiques, et Equation Generale de ces Surfaces. Paris: Mme. Ve Courcier.
[5] Lagrange J.L (1828): Biharmonic Equation for Thin Plates.
[6] Ventsel, E. and Krauthammer, T. (2001): Thin Plates and Shells: Theory, Analysis and Applications. New York: Marwell Publishers Inc.
[7] Cauchy A.L. (1828): Exercises Des Mathematiques, t.3.
[8] Poisson S.D (1829): Memoires De Lâ€™Academie,Vol.III, 1829, pp 357 - 570.
[9] Navier C.L (1823): Sur Les Lois De Lâ€™equilibre et Du Mouvement Des Corps Solides Elastiques (May 1821) Ibid,1823, pp 177 - 183.
[10] Kirchhoff (1850): Uber die Glerchgewieht und die Bewegung einer Elastichen Scheibe, Journal Fur die Reine and Angewandte Mathematik 40, 51 - 88 (in Germain).
[11] Ugural A.C.(1999): Stresses in Plates and Shells (2nd ed.) Singapore: McGraw-Hill.
[12] Okafor, F.O and Oguaghamba, O.(2009): Effects of Flexural Rigidity of Reinforcement Bars on the Fundamental Natural Frequency of Reinforced Concrete Slabs. Nigerian Journal of Technology, Vol. 28(2), pp. 48-57.
[13] Ohya, F.,Ueda,M., Uchiyama, T. and Kikuchi, M. (2005): Free Vibration Analysis by the Superposition Method of Rectangular Mindlin Plates with Internal Columns Resting on Uniform Elastic Supports,http://dx.doi.org/10.1006/jsvi.2005.01.030.
[14] Awodola,T.O, and Omolofe, B,(2014): Response of Concentrated Moving Masses of Elastically Supported Rectangular Plates Resting on Winlker Elastic Foundation, Journal of Theoretical and Applied Mechanics, Sofia,vol.44,No.3,pp65-90.
[15] Agarana, M.C, Gbadeyan, J.A, and Ajayi,O.O(2016): Dynamic Response of Inclined Isotropic Elastic Damped Mindlin Plate Resting on Pasternak Foundation under a Moving Load.Vol.II,IMECS.
[16] Are,E.B, Idowu, A.S, and Gbadeyan, J.A,(2013): Vibration of Damped Simply Supported Orthotropic Rectangular Plates Resting on Elastic Winkler Foundation Subjected to Moving Loads.Advances in Applied Science Research, 4(5), 387-393.
[17] Gbadeyan, J.A,and Dada,M.S(2006): Dynamic Response of a Mindlin Elastic Rectangular Plate under a Distributed Moving Mass. International Journal of Mechanical Science,vol.48 pp 323-340.
[18] Shadnam, M.R, Mofid M. and Akin J.E (2001): On the dynamic Response of Rectangular Plate with Moving Mass. Thin-walled Structures,39, pp797 - 806.
[19] Barile, C., Casavola, C., Vimalathithan, P.K., Pugliese, M., Maiorano, V. (2019): Thermome chanicaland Morphological Studies of CFRP Tested in Different Environmental Conditions. Materials 12(1), 63:1-16.
[20] Guo, X.Y., Wang, Y.L., Huang, P.Y., Zheng, X.H., and Yang, Y. (2019): Fatigue Life Prediction of Reinforced Concrete Beams Strengthened with CFRP:Study Based on an Accumulative Damage Mode. Polymers 11(1),130:1-18.
[21] Guo, X.Y., Yu, B., Huang, P.Y., Zheng, X.H., and Zhao, C. (2018): J-integral approach for main crack propagation of RC beams strengthened with prestressed CFRP under cyclic bending load. Engineering Fracture Mechanics 200:465-478.
[22] Hosseini, A., Ghafoori, E., Al-Mahaidi, R., Zhao, X.L., and Motavalli, M. (2019): Strengthening of a 19th-century roadway metallic bridge using non-prestressed bonded and prestressed unbonded CFRP plates. Construction and Building Materials. 209:240-259.
[23] Ju, M., Oh, H., Sim, J. (2017): Indirect fatigue evaluation of CFRP-reinforced bridge deck slabs under variable amplitude cyclic loading. ksce journal of civil engineering. 21(5):1783-1792.
[24] Li, L.Z., Chen, T., Zhang, N.X. (2019): Test on fatigue repair of central inclined cracked steel plates using different adhesives and CFRP, prestressed and non-prestressed. Composite structures. 216:350-359.
[25] Liang, H.J., Li, S., Lu, Y.Y., Yang, T. (2018): Reliability Analysis of Bond Behaviour of CFRP-Concrete Interface under Wet-Dry Cycles. Materials 11(5), 741:1-14.
[26] Xin Yuan, Wei Zheng, Chaoyu Zhu,Baijian Tang (2020): Fatigue performance and life prediction of CFRP plate in the RC bridge roof reinforcement.Latin American Journal of Solids and Structures, 2020, 17(2), p250