Flutter Characteristics of Cantilevered Non-symmetric Functionally Graded Beams

As a model for flutter analysis of wing of aircrafts, this paper presents a numerical solution for supersonic flutter analysis of cantilevered non-symmetric beams made of functionally graded materials. The propertiesof the beam are considered to be graded through the thickness from two ceramic surfaces at the top and bottom of the beam to an interior metal surface according to two different power law functions. Basedon the Timoshenko beam theory strain energy and kinematic energy are calculated and based on the Piston theory for aerodynamic pressure, work done by external force are calculated. Using Hamilton sprinciple the set of the governing equations and boundary conditions are derived. Dimensionless form of the governing equations and boundary conditions are derived and are solved numerically usingdifferential quadrature method (DQM). Natural frequencies, critical Mach number and flutter frequency are derived. First, convergence and versatility of the presented solution are confirmed andthen effect of thickness, power law index and position of the interior metal surface on the critical Mach number are investigated. Numerical results show that increase in thickness of the beam and volume fractionof the ceramic lead to increase in critical Mach number. It is also shown that among all profiles of variation of properties, the symmetric profile has the biggest value of critical Mach number.