  In this paper, the effect of a centrally located cutout (circular and
elliptical) and cracks emanating from the cutout on the free flexural vibration
behaviour of functionally graded material plates in thermal environment is
studied. The discontinuity surface is represented independent of the mesh by
exploiting the partition of unity method framework. A Heaviside function is
used to capture the jump in the displacement across the discontinuity surface
and asymptotic branch functions are used to capture the singularity around the
crack tip. An enriched shear flexible 4-noded quadrilateral element is used for
the spatial discretization. The properties are assumed to vary only in the
thickness direction. The effective properties of the functionally graded
material are estimated using the Mori- Tanaka homogenization scheme and the
plate kinematics is based on the first order shear deformation theory. The
influence of the plate geometry, the geometry of the cutout, the crack length,
the thermal gradient and the boundary conditions on the free flexural vibration
is numerically studied.
