Numerical analysis of nonlinear free and forced vibrations of buckled curved beams resting on nonlinear elastic foundations

Lacarbonara, 2013 Petyt, 1971, Free vibration of a curved beam, J. Sound Vib., 18, 17, 10.1016/0022-460X(71)90627-4 Ahmed, 1971, Free vibration of curved sandwich beams by the method of finite elements, J. Sound Vib., 18, 61, 10.1016/0022-460X(71)90631-6 Emam, 2004, On the nonlinear dynamics of a buckled beam subjected to a primary-resonance excitation, Nonlinear Dynam., 35, 1, 10.1023/B:NODY.0000017466.71383.d5 Lee, 2006, Anti-symmetric mode vibration of a curved beam subject to autoparametric excitation, J. Sound Vib., 290, 48, 10.1016/j.jsv.2005.03.009 Yoon, 2006, Natural frequencies of thin-walled curved beams, Finite Elem. Anal. Des., 42, 1176, 10.1016/j.finel.2006.05.002 Tomasiello, 2007, A DQ based approach to simulate the vibrations of buckled beams, Nonlinear Dynam., 50, 37, 10.1007/s11071-006-9141-x Luongo, 2008, Analytical and numerical approaches to nonlinear galloping of internally resonant suspended cables, J. Sound Vib., 315, 375, 10.1016/j.jsv.2008.03.067 Nayfeh, 2008, Exact solution and stability of postbuckling configurations of beams, Nonlinear Dynam., 54, 395, 10.1007/s11071-008-9338-2 Emam, 2009, Postbuckling and free vibrations of composite beams, Compos. Struct., 88, 636, 10.1016/j.compstruct.2008.06.006 Emam, 2009, A static and dynamic analysis of the postbuckling of geometrically imperfect composite beams, Compos. Struct., 90, 247, 10.1016/j.compstruct.2009.03.020 Arani, 2011, Curvature effects on thermal buckling load of DWCNT under axial compression force, J. Solid Mech., 3, 1 Arani, 2012, Nonlinear vibration of embedded SWBNNTs based on nonlocal Timoshenko beam theory using DQ method, Physica B, 407, 2549, 10.1016/j.physb.2012.03.065 Hajianmaleki, 2013, Vibrations of straight and curved composite beams: A review, Compos. Struct., 100, 218, 10.1016/j.compstruct.2013.01.001 Yaghoobi, 2013, Post-buckling and nonlinear free vibration analysis of geometrically imperfect functionally graded beams resting on nonlinear elastic foundation, Appl. Math. Model., 37, 8324, 10.1016/j.apm.2013.03.037 Rahimi, 2013, On the postbuckling and free vibrations of FG Timoshenko beams, Compos. Struct., 95, 247, 10.1016/j.compstruct.2012.07.034 Emam, 2013, Approximate analytical solutions for the nonlinear free vibrations of composite beams in buckling, Compos. Struct., 100, 186, 10.1016/j.compstruct.2012.12.044 Ghayesh, 2013, Nonlinear forced vibrations of a microbeam based on the strain gradient elasticity theory, Int. J. Eng. Sci., 63, 52, 10.1016/j.ijengsci.2012.12.001 Farokhi, 2013, Nonlinear dynamics of a geometrically imperfect microbeam based on the modified couple stress theory, Int. J. Eng. Sci., 68, 11, 10.1016/j.ijengsci.2013.03.001 Alijani, 2013, Theory and experiments for nonlinear vibrations of imperfect rectangular plates with free edges, J. Sound Vib., 332, 3564, 10.1016/j.jsv.2013.02.015 Ghayesh, 2014, Coupled longitudinal-transverse behaviour of a geometrically imperfect microbeam, Composites B, 60, 371, 10.1016/j.compositesb.2013.12.030 Sahmani, 2014, Surface energy effects on the free vibration characteristics of postbuckled third-order shear deformable nanobeams, Compos. Struct., 116, 552, 10.1016/j.compstruct.2014.05.035 Shojaei, 2014, Nonlinear forced vibration analysis of postbuckled beams, Arch. Appl. Mech., 84 Ansari, 2014, On the forced vibration analysis of Timoshenko nanobeams based on the surface stress elasticity theory, Compos.: Part B, 60, 158, 10.1016/j.compositesb.2013.12.066 Tang, 2014, Nonlinear modeling and size-dependent vibration analysis of curved microtubes conveying fluid based on modified couple stress theory, Internat. J. Engrg. Sci., 84, 1, 10.1016/j.ijengsci.2014.06.007 Askari, 2015, A unified approach for nonlinear vibration analysis of curved structures using non-uniform rational B-spline representation, J. Sound Vib., 292, 10.1016/j.jsv.2015.05.022 Ansari, 2015, An exact solution for vibrations of postbuckled microscale beams based on the modified couple stress theory, Appl. Math. Model., 39, 3050, 10.1016/j.apm.2014.11.029 Ansari, 2015, An exact solution for the nonlinear forced vibration of functionally graded nanobeams in thermal environment based on surface elasticity theory, ThinWalled Struct., 93, 169 Jafari-Talookolaei, 2016, Vibration characteristics of generally laminated composite curved beams with single through-the-width delamination, Compos. Struct., 138, 172, 10.1016/j.compstruct.2015.11.050 Ansari, 2016, Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro-and nano-beams based on the Mindlin’s strain gradient theory, Appl. Math. Model., 40, 9872, 10.1016/j.apm.2016.06.042 Ansari, 2016, Nonlocal free vibration in the pre- and postbuckled states of magneto-electro-thermoelastic rectangular nanoplates with various edge conditions, Smart Mater. Struct., 25, 095033, 10.1088/0964-1726/25/9/095033 Ansari, 2016, Size-dependent modeling of the free vibration characteristics of postbuckled third order shear deformable rectangular nanoplates based on the surface stress elasticity theory, Composites B, 95, 301, 10.1016/j.compositesb.2016.04.002 Ansari, 2016, Nonlinear primary resonance of third-order shear deformable functionally graded nanocomposite rectangular plates reinforced by carbon nanotubes, Compos. Struct., 154, 707, 10.1016/j.compstruct.2016.07.023 Ansari, 2016, Surface effect on the large amplitude periodic forced vibration of first-order shear deformable rectangular nanoplates with various edge supports, Acta Astronaut., 118, 72, 10.1016/j.actaastro.2015.09.020 Alijani, 2016, Damping for large-amplitude vibrations of plates and curved panels, Part 1: Modeling and experiments, Int. J. Non-Linear Mech., 85, 23, 10.1016/j.ijnonlinmec.2016.05.003 Ansari, 2016, Nonlocal nonlinear first-order shear deformable beam model for post-buckling analysis of magneto-electro-thermo-elastic nanobeams, Sci, Iran. F, 23, 3099 Ansari, 2016, Thermo-electro-mechanical vibration of postbuckled piezoelectric Timoshenko nanobeams based on the nonlocal elasticity theory, Composites B, 89, 316, 10.1016/j.compositesb.2015.12.029 Arefi, 2016, Nonlinear free and forced vibration analysis of embedded functionally graded sandwich micro beam with moving mass, J. Sandwich Struct. Mater. Ghayesh, 2016, Coupled nonlinear dynamics of geometrically imperfect shear deformable extensible microbeams, J. Comput. Nonlinear Dyn., 11 Gholami, 2017, Nonlinear resonant dynamics of geometrically imperfect higher-order shear deformable functionally graded carbon-nanotube reinforced composite beams, Compos. Struct., 174, 45, 10.1016/j.compstruct.2017.04.042 Gholami, 2017, Nonlinear resonance responses of geometrically imperfect shear deformable nanobeams including surface stress effects, Int. J. Non-Linear Mech., 97, 115, 10.1016/j.ijnonlinmec.2017.09.007 delPrado, 2017, Nonlinear vibrations of imperfect fluid-filled viscoelastic cylindrical shells, Procedia Eng., 199, 570, 10.1016/j.proeng.2017.09.175 Zhou, 2016, Precise deflection analysis of laminated piezoelectric curved beam, J. Intell. Mater. Syst. Struct., 27, 2179, 10.1177/1045389X15624797 Mustafa, 2017, Vibration of an axially moving beam supported by a slightly curved elastic foundation, J. Vib. Control Attia, 2017, Nonlinear modeling and analysis of electrically actuated viscoelastic microbeams based on the modified couple stress theory, Appl. Math. Modelling, 41, 195, 10.1016/j.apm.2016.08.036 Quan, 1989, New insights in solving distributed system equations by the quadrature method—I, Anal. Comput. Chem. Eng., 13, 779, 10.1016/0098-1354(89)85051-3 Trefethen, 2000 Keller, 1977, Numerical solution of bifurcation and nonlinear eigenvalue ploblems, Appl. Bifurcation Theory, 359 Calvetti, 2000, Iterative methods for large continuation problems, J. Comput. Appl. Math., 123, 217, 10.1016/S0377-0427(00)00405-2 Nayfeh, 2008