Supersonic flutter analysis of functionally graded material plates with cracks

In this paper, the flutter behaviour of functionally graded material plates immersed in a supersonic flow is studied. An enriched 4-noded quadrilateral element based on field consistency approach is used for this study. The crack is modelled independent of the underlying mesh using partition of unity method (PUM), the extended finite element method (XFEM). The material properties are assumed to be graded only in the thickness direction and the effective material properties are estimated using the rule of mixtures. The plate kinematics is described based on the first order shear deformation theory (FSDT) and the shear correction factors are evaluated employing the energy equivalence principle. The influence of the crack length, the crack orientation, the flow angle and the gradient index on the aerodynamic pressure and the frequency are numerically studied. The results obtained here reveal that the critical frequency and pressure decrease with increase in crack the length and are minimum when the crack is aligned to the flow angle.