[1] Ansari, R., Pourashraf, T., Gholami, R., An exact solution for the nonlinear forced vibration of functionally graded nanobeams in thermal environment based on surface elasticity theory,
Thin-Walled Structures, 93, 2015, pp. 169-176.
[2] Almitani, K. H., Buckling Behaviors of Symmetric and Antisymmetric Functionally Graded Beams,
Journal of Applied and Computational Mechanics, 4(3), 2018, pp. 115-124.
[3] Eltaly, B., Structural performance of notch damaged steel beams repaired with composite materials,
International Journal of Advanced Structural Engineering, 8(2), 2016, pp. 119–131.
[4] Lee, Y. Y., Su, R. K. L., Ng, C. F., Hui, C. K., The effect of modal energy transfer on the sound radiation and vibration of a curved panel: Theory and experiment,
Journal of Sound and Vibration, 324, 2009, pp. 1003-1015.
[5] Meziane, M. A. A., Abdelaziz, H. H., Tounsi, A., An efficient and simple refined theory for buckling and free vibration of exponentially graded sandwich plates under various boundary conditions,
Journal of Sandwich Structures & Materials, 16(3), 2014, pp. 293-318.
[6] Mahapatra, T. R., Kar, V. R., Panda, S. K., Large amplitude vibration analysis of laminated composite spherical panels under hygrothermal environment,
International Journal of Structural Stability and Dynamics, 16(3), 2016, 1450105.
[7] Mahapatra, T. R., Kar, V. R., Panda, S. K., Nonlinear free vibration analysis of laminated composite doubly curved shell panel in hygrothermal environment,
Journal of Sandwich Structures & Materials, 17(5), 2015, pp. 511-545.
[8] Panda, S. K., Mahapatra, T. R., Nonlinear finite element analysis of laminated composite spherical shell vibration under uniform thermal loading,
Meccanica, 49(1), 2014, pp. 191-213.
[9] Mehar, K., Panda, S. K., Geometrical nonlinear free vibration analysis of FG-CNT reinforced composite flat panel under uniform thermal field,
Composite Structures, 143, 2016, pp. 336-346.
[10] Mehar, K., Panda, S. K., Dehengia, A., Kar, V. R., Vibration analysis of functionally graded carbon nanotube reinforced composite plate in thermal environment,
Journal of Sandwich Structures & Materials, 18(2), 2015, pp. 151-173.
[11] Hadji, L., Khelifa, Z., Abbes, A. B. E., A New Higher Order Shear Deformation Model for Functionally Graded Beams,
KSCE Journal of Civil Engineering, 20(6), 2015, pp. 1-7.
[12] Ghasemi, A. R., Taheri-Behrooz, F., Farahani, S. M. N., Mohandes, M., Nonlinear free vibration of an Euler-Bernoulli composite beam undergoing finite strain subjected to different boundary conditions,
Journal of Vibration and Control, 22(3), 2016, pp. 799–811.
[13] Reddy, J. N., Khodabakhshi, P., A unified beam theory with strain gradient effect and the von Karman nonlinearity,
ZAMM Zeitschrift für Angewandte Mathematik und Mechanik, 97(1), 2017, pp. 70-91.
[14] Chen, W., Wu, Z., A new higher-order shear deformation theory and refined beam element of composite laminates,
Acta Mechanica Sinica, 21, 2005, pp. 65–69.
[15] Reddy, J. N., Mahaffey, P., Generalized beam theories accounting for von Kármán nonlinear strains with application to buckling,
Journal of Coupled Systems and Multiscale Dynamics, 1(1), 2013, pp. 120-134.
[16] Panda, S. K., Singh, B. N., Nonlinear free vibration of spherical shell panel using higher order shear deformation theory–a finite element approach,
International Journal of Pressure Vessels and Piping, 86 (6), 2009, pp. 373-383.
[17] Singh, V. K., Panda, S. K., Nonlinear free vibration analysis of single/doubly curved composite shallow shell panels,
Thin-Walled Structures, 85, 2014, pp. 341-349.
[18] Kar, V. R., Panda, S. K., Nonlinear free vibration of functionally graded doubly curved shear deformable panels using finite element method,
Journal of Vibration and Control, 22(7), 2016, pp. 1935-1949.
[19] Panda, S. K., Singh, B. N., Nonlinear free vibration analysis of thermally post-buckled composite spherical shell panel,
International Journal of Mechanics and Materials in Design, 6(2), 2010, pp. 175-188.
[20] Panda, S. K., Singh, B. N., Non-linear free vibration analysis of laminated composite cylindrical/hyperboloid shell panels based on higher-order shear deformation theory using non-linear finite-element method,
Proceedings of the Institution of Mechanical Engineers, Part G: Journal of Aerospace Engineering, 222(7), 2008, pp. 993-1006.
[21] Mehar, K., Panda, S. K., Bui, T. Q., Mahapatra, T. R., Nonlinear thermoelastic frequency analysis of functionally graded CNT-reinforced single/doubly curved shallow shell panels by FEM,
Journal of Thermal Stresses, 40(7), 2017, pp. 899-916.
[22] Mahapatra, T. R., Panda, S. K., Nonlinear free vibration analysis of laminated composite spherical shell panel under elevated hygrothermal environment: A micromechanical approach,
Aerospace Science and Technology, 49, 2016, pp. 276-288.
[23] Kar, V. R., Panda, S. K., Geometrical nonlinear free vibration analysis of FGM spherical panel under nonlinear thermal loading with TD and TID properties,
Journal of Thermal Stresses, 39(8), 2016, pp. 942-959.
[24] Kar, V. R., Panda, S. K., Free vibration responses of temperature dependent functionally graded curved panels under thermal environment,
Latin American Journal of Solids and Structures, 12(11), 2015, pp. 2006-2024.
[25] Panda, S. K., Singh, B. N., Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel embedded with SMA fibers,
Nonlinear Dynamics, 74(1-2), 2013, pp. 395-418.
[26] Hirwani, C. K., Panda, S. K., Numerical nonlinear frequency analysis of pre-damaged curved layered composite structure using higher-order finite element method,
International Journal of Non-Linear Mechanics, 102, 2018, pp. 14-24.
[27] Hirwani, C. K., Mahapatra, T. R., Panda, S. K., Sahoo, S. S., Singh, V. K., Patle, B. K., Nonlinear free vibration analysis of laminated carbon/epoxy curved panels,
Defence Science Journal, 67(2), 2017, pp. 207-2018.
[28] Kaci, A., Houari, M. S. A., Bousahla, A. A., Tounsi, A., Mahmoud, S. R., Post-buckling analysis of shear-deformable composite beams using a novel simple two-unknown beam theory,
Structural Engineering and Mechanics, 65(5), 2018, pp. 621-631.
[29] Bourada, M., Kaci, A., Houari, M. S. A., Tounsi, A., A new simple shear and normal deformations theory for functionally graded beams,
Steel and Composite Structures, 18(2), 2015, pp. 409–423.
[30] Bounouara, F., Benrahou, K. H., Belkorissat, I., Tounsoi, A., A nonlocal zeroth-order shear deformation theory for free vibration of functionally graded nanoscale plates resting on elastic foundation,
Steel and Composite Structures, 20(2), 2016, pp. 227-249.
[31] Bellifa, H., Benrahou, K.H., Bousahla, A. A., Tounsi, A., Mahmoud, S. R., A nonlocal zeroth-order shear deformation theory for nonlinear postbuckling of nanobeams,
Structural Engineering and Mechanics, 62(6), 2017, pp. 695 - 702.
[32] Bouafia, K., Kaci, A., Houari, M. S. A., Benzair, A., Tounsi, A., A nonlocal quasi-3D theory for bending and free flexural vibration behaviors of functionally graded nanobeams,
Smart Structures and Systems, 19(2), 2017, pp. 115-126.
[33] Mouffoki, A., Bedia, E. A. A., Houari, M. S. A., Tounsi, A., Hassan, S. , Vibration analysis of nonlocal advanced nanobeams in hygro-thermal environment using a new two-unknown trigonometric shear deformation beam theory,
Smart Structures and Systems, 20(3), 2017, pp. 369-383.
[34] Attia, A. Bousahla, A. A., Tounsi, A., Mahmoud, S. R., Alwabli, A. S., A refined four variable plate theory for thermoelastic analysis of FGM plates resting on variable elastic foundations,
Structural Engineering and Mechanics, 65(4), 2018, pp. 453-464.
[35] Azrar, L., Benamar, R., White, R. G., A semi-analytical approach to the nonlinear dynamic response problem of beams at large vibration amplitudes, Part II: multimode approach to the steady state forced periodic response,
Journal of Sound and Vibration,255(1), 2002, pp. 1–41.
[36] Panda, S. K., Singh, B. N., Large amplitude free vibration analysis of thermally post-buckled composite doubly curved panel using nonlinear FEM,
Finite Elements in Analysis and Design, 47(4), 2011, pp. 378-386.
[37] Hirwani, C. K., Patil, R. K., Panda, S. K., Mahapatra, S. S., Mandal, S. K., Srivastava, L., Buragohain, M. K., Experimental and numerical analysis of free vibration of delaminated curved panel,
Aerospace Science and Technology, 54, 2016, pp. 353-370.
[38] Wickert, J. A., Non-linear vibration of a traveling tensioned beam,
International Journal of Non-Linear Mechanics, 27, 1992, pp. 503–517.
[39] Nayfeh, A. H.,
Introduction to Perturbation Techniques, John Wylie, 1993.
[40] Fooladi, M., Abaspour, S. R., Kimiaeifar, A., Rahimpour, M., (2009) On the Analytical Solution of Kirchhoff Simplified Modelfor Beam by using of Homotopy Analysis Method,
World Applied Sciences Journal, 6, 2009, pp. 297-302.
[41] Liao, S. J.,
The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D. Thesis, Shanghai Jiao Tong University, 1992.
[42] Moeenfard, H., Mojahedi, M., Ahmadian, M. T., A homotopy perturbation analysis of nonlinear free vibration of Timoshenko micro beams,
Journal of Mechanical Science and Technology, 25, 2011, pp. 557-565.
[43] Younesian, D., Saadatnia, Z., Askari, H., Analytical solutions for free oscillations of beams on nonlinear elastic foundations using the variational iteration method,
Journal of Theoretical and Applied Mechanics, 50, 2012, pp. 639-652.
[44] Mickens, R. E., A generalization of the method of harmonic balance,
Journal of Sound and Vibration, 111, 1986, pp. 515-518.
[45] Rahman, M. S., Haque, M. E., Shanta, S. S., Harmonic Balance Solution of Nonlinear Differential Equation (Non-Conservative),
Journal of Advances in Vibration Engineering, 9(4), 2010, pp. 345-356.
[46] Lee, Y. Y., Analytic Solution for Nonlinear Multimode Beam Vibration Using a Modified Harmonic Balance Approach and Vieta’s Substitution,
Shock and Vibration, 2015, Article ID 3462643, 6 pages.
[47] Foda, M. A., Analysis of large amplitude free vibrations of beams using the KBM method,
Journal of Engineering and Applied Science, 42, 1995, pp. 125-138.
[48] Coskun, I., Engin, H., Non-linear vibrations of a beam on an elastic foundation,
Journal of Sound and Vibration,223(3), 1999, pp. 335-354.
[49] Peng, J. S., Liu, Y., Yang, J., A semi-analytical method for nonlinear vibration of Euler-Bernoulli beams with general boundary conditions,
Mathematical Problems in Engineering, 2010, Article ID 591786, 17 pages.
[50] Pirbodaghi, T., Ahmadian, M. T., Fesanghary, M., On the homotopy analysis method for non-linear vibration of beams,
Mechanics Research Communications, 36, 2009, pp. 143–148.
[49] Sedighi, H. M., Shirazi, K. H., Zare, J., An analytic solution of transversal oscillation of quintic non-linear beam with homotopy analysis method,
International Journal of Non-Linear Mechanics, 47, 2012, pp. 777-784.
[52] Motallebi, A. A., Poorjamshidian, M., Sheikh, J., Vibration analysis of a nonlinear beam under axial force by homotopy analysis method,
Journal of Solid Mechanics, 6, 2014, pp. 289-298.
[53] Sedighi, H. M., Daneshmand, F., Nonlinear transversely vibrating beams by the homotopy perturbation method with an auxiliary term,
Journal of Applied and Computational Mechanics, 1(1), 2015, pp. 1-9.
[54] Baghani, M., Jafari-Talookolaei, R. A., Salarieh, H., Large amplitudes free vibrations and post-buckling analysis of unsymmetrically laminated composite beams on nonlinear elastic foundation,
Applied Mathematical Modelling, 35, 2011, pp. 130–138.
[55] 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, 2011, pp. 571-583.
[56] Yaghoobi, H., Torabi, M., An Analytical Approach to Large Amplitude Vibration and Post-Buckling of Functionally Graded Beams Rest on Non-Linear Elastic Foundation,
Journal of Theoretical and Applied Mechanics, 51(1), 2013, pp. 39-52.
[57] Yaghoobi, H., Torabi, M., Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation,
Applied Mathematical Modelling, 37, 2013, 8324–8340.
[58] Kanani, A. S., Niknam, H., Ohadi, A. R., Aghdam, M. M., Effect of nonlinear elastic foundation on large amplitude free and forced vibration of functionally graded beam,
Composite Structures, 115, 2014, pp. 60–68
[59] Hasan, A. S. M. Z., Lee, Y. Y., Leung, A. Y. T., The multi-level residue harmonic balance solutions of multi-mode nonlinearly vibrating beams on an elastic foundation,
Journal of Vibration and Control, 22(14), 2016, pp. 3218-3235.
[60] Rahman, M. S., Lee, Y. Y., New modified multi-level residue harmonic balance method for solving nonlinearly vibrating double-beam problem,
Journal of Sound and Vibration,406, 2017, pp. 295-327.