The nonlinear unsymmetrically laminated composite beams on Winkler-Pasternak fundation

Authors

  • Bogdan Marinca Politehnica University Timisoara
  • Vasile Marinca Politehnica University Timisoara. Center for Advances and Fundamental Technical Research, Romanian Academy, Timisoara Branch, Bd. M.Viteazul Nr. 24, 300233, Timisoara Romania

Keywords:

Nonlinear equations, composite beam, OPIM

Abstract

In this study, Optimal Parametric Iteration Method (OPIM) is presented for large amplitude free vibrations of nonlinear unsymmetrically laminated composite beams on Winkler – Pasternak elastic foundation. Based on von Kárman geometric nonlinearity, on Euler – Bernoulli beam theory and Galerkin procedure, we obtain a second-order nonlinear differential equation with quadratic and cubic terms. Comparison between results of the present work and those of numerical results shows the accuracy of our approach.

References

CENGIZ DOKMECI, M., High-frequency thermoviscoelastic of functionally graded thin beams, The Journal of the Acoustic Society of America, 119, 3336, 2006.

KARAMI KHORAMABADI, M., Free vibration of functionally graded beams with piezoelectric layers subjected to axial load, Journal of Solid Mechanics, pp. 22-28, 2009.

YOUNESIAN, D., ESMAILZADEH, E., Non-linear vibration of variable speed rotating viscoelastic beams, Nonlinear Dynamics, 60, pp. 193-205, 2010.

FALLAH, A., AGHDAM, M. M., Nonlinear free vibration and post-buckling analysis of functionally graded beams on nonlinear elastic foundation, European Journal of Mechanics-A/Solids. 30, pp. 571-583, 2011.

BAGHANI, M., TALOOKOLAEI, R. A. J., SALARIEH, H., Large amplitudes free vibrations and post-buckling analysis of unsymmetrical laminated composite beams on nonlinear elastic foundation, Applied Math. Modelling, 15, pp. 130-138, 2011.

CHALLAMEL, N., GIRHAMMAR, U. A., Variationally-based theories for buckling of partial composite-beam-columns including shear and axial effects, Engineering Structures, 33, pp. 2297-2319, 2011.

EMAM SAMIR, A., Analysis of shear-deformable composite beams in postbuckling, Composite Structures, 94, pp. 24-30, 2011.

SU, H., BANERJEE, J. R., Free vibration of a functionally graded Timoshenko beam using the dynamic stifness method, Proceedings of the Eleventh Int. Conf. on Comput. Structures Tech., Scotland, paper 102, 2012.

THOMAS, B., INAMDAR, P., ROY, T., NANDA, B. K., Finite element modeling and free vibration analysis of functionally graded nanocomposite beams reinforced by randomly oriented carbon monotubes, Int. J. Theoretical and Applied Research in Mech. Eng., 2, pp. 97-109, 2013.

YAGHOOBI, H., TORABI, M., An analytical approach to large amplitude vibration and post buckling of functionally graded beams rest on non-linear elastic foundation, J. of Theoretical and Applied Mechanics, 51, pp. 39-52, 2013.

AKBAS, S. D., Free vibration and bending of functionally graded beams resting on elastic foundation, Research on Engineering Structures and Materials, 1, pp. 25-37, 2015.

ELMAGUIRI, M. H., HATERBOUCH, M., BOUAYAD, A., OUSSOUADDI, D, Geometrically nonlinear free vibration of functionally graded beams, J. Mater. Environ. Sci., 6, pp. 3620-3633, 2019.

EBRAHIMI, F., MOKHTARI, M., Free vibration analysis of a rotating Mori-Tanaka-based functionally graded beam via differential transformation method, Arab. J. Sci. Eng., DOI 10.1007/s13369-015-1689-7, 2015.

HEIN, H., FEKLISOVA, L., Free vibrations of non-uniform and axially functionally graded beams using Haar wavelets, Eng. Structures, , 2011.

MARINCA, V., HERISANU, N., The nonlinear thermomechanical vibration of a functionally graded beam on Winkler-Pasternak foundation, MATEC Web of Conf. 148, 13004, 2018.

MARINCA, V., HERISANU, N., Analytical approach to the dynamic analysis of a rotating elastic machine, Comput. Math. Appl., 58, pp. 2320-2324, 2009.

MARINCA, V., HERISANU, N., Nonlinear Dynamical Systems in Engineering. Some Approximate Approach, Springer, 2015.

Published

2021-12-29