Supersonic Flutter Analysis of Cantilevered Functionally Graded Sandwich Thick Plates

In this paper, flutter analysis of cantilevered functionally graded (FG) sandwich plates imposed to an external supersonic flows is investigated. The plate is composed of three layers: an isotropic homogeneous(metallic) core and two symmetric FG face sheets whose properties vary from ceramic-rich exterior layers to interior metal-rich ones according to a power law function. The plate is modeled mathematicallybased on the first order shear deformation theory(Mindlin-Reissner model) and aerodynamic pressure is estimated using linear supersonic Piston theory. The total strain energy, kinetic one and work done byexternal forces (aerodynamic pressure) are calculated and using Hamilton s principle, the set of governing equations and external boundary conditions are derived. The dimensionless form of the governingequations and boundary condition are solved numerically using differential quadrature method (DQM) and natural frequencies are obtained. Convergence and versatility of the solution are testedand natural frequencies, damping ratio, corresponding mode shapes, critical aerodynamic pressure and flutter frequency are calculated and compared with those presented by other authors. Effect of thickness of thecore and power law index on the critical aerodynamic pressure and flutter frequency are investigated. Results show that with increase in volume fraction of the ceramic part, flutter boundaries are extended and platebecomes more stable. Results of this paper can be considered as a useful tool for design wings and tail fins of aircrafts.