Free Vibration Analysis of Nonlinear Circular Plates Resting on Winkler and Pasternak Foundations

Subject Areas : Engineering

M.G Sobamowo ¹ , S.A Salawu ²

1 - Department of Mechanical Engineering, University of Lagos, Akoka, Lagos, Nigeria
2 - Department of civil and Environmental Engineering, University of Lagos, Akoka, Nigeria

Received: 2019-11-05 Accepted : 2020-01-04 Published : 2020-03-01

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References:

[1] Andrea R.D., Silva A., Ricardo A.M., Silveira A., Paulo B., Gonc-Balves B., 2001, Numerical methods for analysis of plates on tensionless elastic foundations, International Journal of Solids and Structures-Pergamon 38: 2083-2100.
[2] Lamb H., 2016, On the vibrations of an elastic plate in contact with water, Proceedings of the Royal Society of London , Series A 98: 205-216.
[3] Raoa L.B., Raob C.K., 2018, Vibrations of circular plates resting on elastic foundation with elastically restrained edge against translation, The Journal of Engineering Research 15(1): 14-25.
[4] Haojiang D., Rongqiao X., Weiqiu C., 2000, Exact solutions for free vibration of transversely isotropic piezoelectric circular plates, Acta Mechanica Sinica 16(2): 141-147.
[5] Soni S., Jain N.K., Joshi P.V., 2017, Aanalytical modeling for non-linear vibration analysis of functionally graded plate submerged in fluid, Indian Journal of Science Research 4(2): 229-236.
[6] Kumar S., Prashar P., 2015, Energy method to analysis the vibration of orthotropic circular plate with bi-dimensional thickness variation, International Journal of Applied Research 1(12): 829-835.
[7] Siddiqul A.M., Haroon T., Bhatti S., Ansari A.R., 2011, A comparison of the adomian and homotopy perturbation methods in solving the problem of squeezing flow between two circular plates, Mathematical Modelling and Analysis 15(4): 491-504.
[8] Yin-Shan Y., Temuer C., 2015, Application of the Homotopy perturbation method for the large deflection problem of a circular plate, Applied Mathematical Modelling 39: 1308-1316.
[9] Rostamiyan Y., Fereidoon A., Davoudabadi M.R., Yag H., 2010, Analytical approach to investigation of deflection of circular plate under uniform load by Homotopy perturbation method, Mathematical and Computational Applications 15(5): 816-821.
[10] Yalcin H.S., Arikoglu A., Ozkol I., 2009, Free vibration analysis of circular plates by differential transformation method, Applied Mathematics and Computation 212: 377-386.
[11] Xiao-Jing Z., 1987, On exact solution of karman's equations of rigid clamped circular plate and shallow spherical shell under a concentrated load, Applied Mathematics and Mechanics 8(11): 1057-1068.
[12] Shariyat M., Alipour M.M., 2011, Differential transform vibration and modal stress analyses of circular plates made of two-directional functionally graded materials resting on elastic foundations, Archive Applied Mechanism 81: 1289-1306.
[13] Leissa A.W., 1970, Vibration of Plates, National Aeronautics and Space Adminstration, Washington.
[14] Wu T.Y., Wung T.Y., Liu G.R., 2002, Free vibration analysis of circular plate using generalize differential quadrature rule, Computer Methods in Applied Mechanics and Engineering 191: 5365-5380.