Free vibration and stability analysis of axially functionally graded tapered Timoshenko beams with classical and non-classical boundary conditions
Tài liệu tham khảo
Kim, 2002, Finite element evaluation of mixed mode stress intensity factors in functionally graded materials, Int J Numer Meth Eng, 53, 1903, 10.1002/nme.364
Wakashima, 1990, Space applications of advanced structural materials, ESA, SP-303, 97
Benatta, 2009, Mathematical solution for bending of short hybrid composite beams with variable fibers spacing, Appl Math Comput, 212, 337, 10.1016/j.amc.2009.02.030
Li, 2008, A unified approach for analyzing static and dynamic behaviors of functionally graded Timoshenko and Euler–Bernoulli beams, J Sound Vib, 318, 1210, 10.1016/j.jsv.2008.04.056
Li, 2010, Large deflections of a non-linear cantilever functionally graded beam, J Reinf Plast Compos, 29, 1761, 10.1177/0731684409103340
Catellani, 2004, Apparently first closed-form solutions of semi-inverse buckling problems involving distributed and concentrated loads, Thin Wall Struct, 42, 1719, 10.1016/j.tws.2004.05.007
Neuringer, 2001, Inhomogeneous beams that may possess a prescribed polynomial second mode, Chaos Soliton Fract, 12, 881, 10.1016/S0960-0779(00)00043-6
Wu, 2005, Semi-inverse for axially functionally graded beams with an anti-symmetric vibration mode, J Sound Vib, 284, 1190, 10.1016/j.jsv.2004.08.038
Guede, 2001, A fifth-order polynomial that serves as both buckling and vibration mode of an inhomogeneous structure, Chaos Soliton Fract, 12, 1267, 10.1016/S0960-0779(00)00014-X
Guede, 2001, Apparently the first closed-form solution for inhomogeneous vibrating beams under axial loading, Proc Roy Soc A, 457, 623, 10.1098/rspa.2000.0685
Elishakoff, 2001, Apparently first closed-form solution for vibrating inhomogeneous beams, Int J Solids Struct, 38, 3411, 10.1016/S0020-7683(00)00266-3
Elishakoff, 2004, Analytical polynomial solutions for vibrating axially graded beams, Mech Adv Mater Struct, 11, 517, 10.1080/15376490490452669
Aydogdu, 2008, Semi-inverse method for vibration and buckling of axially functionally graded beams, J Reinf Plast Compos, 27, 683, 10.1177/0731684407081369
Singh, 2009, Buckling of functionally graded and elastically restrained non-uniform columns, Composite: Part B, 40, 393, 10.1016/j.compositesb.2009.03.001
Shahba A, Attarnejad R, Hajilar S. Free vibration and stability of axially functionally graded tapered Euler–Bernoulli beams. Shock Vib, doi:10.3233/SAV-2010-0589.
Huang, 2010, A new approach for free vibration of axially functionally graded beams with non-uniform cross-section, J Sound Vib, 329, 2291, 10.1016/j.jsv.2009.12.029
Attarnejad R, Shahba A. Basic displacement functions for centrifugally stiffened tapered beams. Commun Numer Meth Eng, doi:10.1002/cnm.1365.
Attarnejad, 2010, Basic displacement functions in analysis of non-prismatic beams, Eng Comput, 27, 733, 10.1108/02644401011062117
Elishakoff, 2001, Euler’s problem revisited: 222years later, Meccanica, 36, 265, 10.1023/A:1013974623741
Banerjee, 1985, Exact Bernoulli–Euler dynamic stiffness matrix for a range of tapered beam, Int J Numer Meth Eng, 21, 2289, 10.1002/nme.1620211212
Attarnejad R, Shahba A. Dynamic basic displacement functions in free vibration analysis of centrifugally stiffened tapered beams: a mechanical solution. Meccanica, doi:10.1007/s11012-010-9383-z.
Bazoune, 2003, Shape functions of three-dimensional Timoshenko beam element, J Sound Vib, 259, 473, 10.1006/jsvi.2002.5122
Cleghorn, 1992, Finite element formulation of a tapered Timoshenko beam for free lateral vibration analysis, J Sound Vib, 152, 461, 10.1016/0022-460X(92)90481-C
Attarnejad R, Shahba A, Semnani SJ. Analysis of non-prismatic Timoshenko beams using basic displacement functions. Adv Struct Eng 2011.
Attarnejad, 2010, Basic displacement functions for free vibration analysis of non-prismatic Timoshenko beams, Finite Elem Anal Des, 46, 916, 10.1016/j.finel.2010.06.005
Tong, 1995, Vibration analysis of Timoshenko beams with non-homogeneity and varying cross-section, J Sound Vib, 186, 821, 10.1006/jsvi.1995.0490
Sorrentino, 2007, Analysis of non-homogeneous Timoshenko beams with generalized damping distributions, J Sound Vib, 304, 779, 10.1016/j.jsv.2007.03.038
Sklyar, 2008, Spectral properties of non-homogeneous Timoshenko beam and its rest to rest controllability, J Math Anal Appl, 338, 1054, 10.1016/j.jmaa.2007.05.058
Reddy, 2002
Nakamura, 2000, Determination of properties of graded materials by inverse analysis and instrumented indentation, Acta Mater, 48, 4293, 10.1016/S1359-6454(00)00217-2
Leung, 2001, Dynamic stiffness for piecewise non-uniform Timoshenko column by power series-part I: Conservative axial force, Int J Numer Meth Eng, 51, 505, 10.1002/nme.159.abs
Wang, 2004