FGM	Functionally graded materials
FG	Functionally graded
DSM	Dynamic stiffness matrix
DS	Dynamic stiffness
NLTD	Non-linear temperature distribution
TBT	Timoshenko beam theory
A	cross-sectional area
Pm	material properties of metal
Pc	material properties of ceramic
Vm	volume fraction of metal
Vc	volume fraction of ceramic
k	power law index
K	thermal conductivity
$R_i,R_o$	inner and outer radius of the FG rotor
$T_i,T_o$	temperature at inner and outer surface of the FG rotor
$K_i,K_o$	thermal conductivity at inner and outer surface of the FG rotor
(x,y,s)	coordinate system
u, v	lateral deflections in (x,s) and (y,s) planes, respectively
${\theta }_x,{\theta }_y$	bending slopes in (y,s) and (x,s) planes, respectively,
$q_x,q_y$	distributed transverse force (x,s) and (y,s) planes, respectively, based on translation inertia
$Q_x,Q_y$	distributed moments in (y,s) and (x,s) planes, respectively, based on rotation inertia and gyroscopic moments
$T_x,T_y$	shear forces in (x,s) and (y,s) planes, respectively, based on transverse shear effects
$M_x,M_y$	bending moments in (y,s) and (x,s) planes, respectively
E	Young’s modulus
$\nu$	Poisson’s ratio
G	shear modulus
$\kappa$	shear factor
$\rho$	density
$I_d$	diametric mass moment of inertia of the disk
$I_p$	polar mass moment of inertia of the disk
d	rotor diameter
L	rotor or beam length
l	element length
R	radial distance