E	Euclidean space	${\lambda }_c$	Nonlocal parameter
L	Length of FG nanobeam	${\nu }^B, {\nu }^S$	Poisson’s ratios of the bulk and surface layer
Σ	Generic cross-section	n	material gradient index
∂Σ	Perimeter of Σ	$E_c$	Young’s modulus ceramic
{$O,x,y, z$}	Cartesian coordinate system	$E_m$	Young’s modulus metal
O	Geometric center of Σ	${\rho }_c$	Mass density of ceramic
x	Axis of FG nanobeam	${\rho }_m$	Mass density of metal
y, z	Principal axes of geometric inertia of Σ	$E_c^S$	Surface Young modulus of ceramic
b, h	Width and thickness Σ	$E_m^S$	Surface Young modulus of metal
R	Radius of Σ	${\rho }_c^S$	Surface mass density of ceramic
B, S	Bulk and surface layers of FG material	${\rho }_m^S$	Surface mass density of metal
E	Euclidean space	${\tau }_c^S$	Residual surface stress of ceramic
L	Length of FG nanobeam	${\tau }_m^S$	Residual surface stress of metal