Free vibration characteristics of a functionally graded beam by finite element method

Chen, 2004, Buckling of rectangular functionally graded material plates subjected to nonlinearly distributed in-plane edge loads, Smart Mater. Struct., 13, 1430, 10.1088/0964-1726/13/6/014

Aydogdu, 2007, Free vibration analysis of functionally graded beams with simply supported edges, Mater. Des., 28, 1651, 10.1016/j.matdes.2006.02.007

Cheng, 2000, Exact correspondence between eigenvalues of membranes and functionally graded simply supported polygonal plates, J. Sound Vib., 229, 879, 10.1006/jsvi.1999.2525

Sankar, 2001, An elasticity solution for functionally graded beams, Compos. Sci. Technol., 61, 689, 10.1016/S0266-3538(01)00007-0

Chakraborty, 2003, A new beam finite element for the analysis of functionally graded materials, Int. J. Mech. Sci., 45, 519, 10.1016/S0020-7403(03)00058-4

Goupee, 2006, Optimization of natural frequencies of bidirectional functionally graded beams, Struct. Multidiscip. Optim., 32, 473, 10.1007/s00158-006-0022-1

Lu, 2008, Semi-analytical elasticity solutions for bi-directional functionally graded beams, Int. J. Solids Struct., 45, 258, 10.1016/j.ijsolstr.2007.07.018

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

Xiang, 2008, Free and forced vibration of a laminated FGM Timoshenko beam of variable thickness under heat conduction, Composites: Part B, 39, 292, 10.1016/j.compositesb.2007.01.005

Ying, 2008, Two-dimensional elasticity solutions for functionally graded beams resting on elastic foundations, Compos. Struct., 84, 209, 10.1016/j.compstruct.2007.07.004

Kapuria, 2008, Bending and free vibration response of layered functionally graded beams: a theoretical model and its experimental validation, Compos. Struct., 82, 340, 10.1016/j.compstruct.2007.01.019

Piovan, 2009, A study on the dynamics of rotating beams with functionally graded properties, J. Sound Vib., 327, 134, 10.1016/j.jsv.2009.06.015

Sina, 2009, An analytical method for free vibration analysis of functionally graded beams, Mater. Des., 30, 741, 10.1016/j.matdes.2008.05.015

Oyekoya, 2009, Buckling and vibration analysis of functionally graded composite structures using the finite element method, Compos. Struct., 89, 134, 10.1016/j.compstruct.2008.07.022

Simsek, 2009, Free and forced vibration of a functionally graded beam subjected to a concentrated moving harmonic load, Compos. Struct., 90, 465, 10.1016/j.compstruct.2009.04.024

Simsek, 2010, Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Compos. Struct., 92, 904, 10.1016/j.compstruct.2009.09.030

Malekzadeh, 2010, Out-of-plane free vibration of functionally graded circular curved beams in thermal environment, Compos. Struct., 92, 541, 10.1016/j.compstruct.2009.08.040

Ke, 2010, Nonlinear free vibration of functionally graded carbon nanotube-reinforced composite beams, Compos. Struct., 92, 676, 10.1016/j.compstruct.2009.09.024

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

Meirovitch, 1970