TY - JOUR
T1 - Size-dependent free flexural vibration behavior of functionally graded nanoplates
AU - Natarajan, Sundararajan
AU - Chakraborty, S.
AU - Thangavel, M.
AU - Bordas, S.
AU - Rabczuk, Timon
PY - 2012/12
Y1 - 2012/12
N2 - In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are approximated by non-uniform rational B-splines. The nonlocal constitutive relation is based on Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate. From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length.
AB - In this paper, size dependent linear free flexural vibration behavior of functionally graded (FG) nanoplates are investigated using the iso-geometric based finite element method. The field variables are approximated by non-uniform rational B-splines. The nonlocal constitutive relation is based on Eringen's differential form of nonlocal elasticity theory. The material properties are assumed to vary only in the thickness direction and the effective properties for the FG plate are computed using Mori-Tanaka homogenization scheme. The accuracy of the present formulation is demonstrated considering the problems for which solutions are available. A detailed numerical study is carried out to examine the effect of material gradient index, the characteristic internal length, the plate thickness, the plate aspect ratio and the boundary conditions on the global response of the FG nanoplate. From the detailed numerical study it is seen that the fundamental frequency decreases with increasing gradient index and characteristic internal length.
KW - Eringen's gradient elasticity
KW - Finite element
KW - Functionally graded
KW - Internal length
KW - Mori-Tanaka
KW - NURBS
KW - Partition of unity
UR - http://www.scopus.com/inward/record.url?scp=84864400929&partnerID=8YFLogxK
U2 - 10.1016/j.commatsci.2012.06.031
DO - 10.1016/j.commatsci.2012.06.031
M3 - Article
AN - SCOPUS:84864400929
SN - 0927-0256
VL - 65
SP - 74
EP - 80
JO - Computational Materials Science
JF - Computational Materials Science
ER -