  A novel and effective formulation that combines the eXtended IsoGeometric
Approach (XIGA) and Higher-order Shear Deformation Theory (HSDT) is proposed to
study the free vibration of cracked Functionally Graded Material (FGM) plates.
Herein, the general HSDT model with five unknown variables per node is applied
for calculating the stiffness matrix without needing Shear Correction Factor
(SCF). In order to model the discontinuous and singular phenomena in the
cracked plates, IsoGeometric Analysis (IGA) utilizing the Non-Uniform Rational
B-Spline (NURBS) functions is incorporated with enrichment functions through
the partition of unity method. NURBS basis functions with their inherent
arbitrary high order smoothness permit the C1 requirement of the HSDT model.
The material properties of the FGM plates vary continuously through the plate
thickness according to an exponent function. The effects of gradient index,
crack length, crack location, length to thickness on the natural frequencies
and mode shapes of simply supported and clamped FGM plate are studied.
Numerical examples are provided to show excellent performance of the proposed
method compared with other published solutions in the literature.
