Flutter analysis of honeycomb sandwich trapezoidal wings reinforced with GPLs

Abstract

Flutter analysis of honeycomb sandwich trapezoidal wings subjected to supersonic airflow is investigated. It is assumed that the sandwich trapezoidal wing is made of an orthotropic honeycomb core surrounded by two face sheets which are reinforced with graphene platelets (GPLs). Applying the Hamilton’s principle, the governing equations of motion based on the first-order shear deformation theory (FSDT) are derived in the Cartesian coordinates. Using a mapping, these equations are converted from Cartesian coordinates to trapezoidal coordinates. Then, the transformed partial differential equations are discretized using generalized differential quadrature (GDQ) method and solved by the state space technique. The influences of various parameters such as the geometry of trapezoidal wings and hexagonal cells, GPLs distribution patterns and the weight fraction of GPLs on the stability region are investigated in detail. It is concluded that the internal geometrical parameters of the hexagonal core have no significant effects on the stability region of the wing. Furthermore, adding a slight percent of GPLs into polymer matrix of face sheets has an enormous effect on the stability region. So that, by adding just 0.5%, 1% and 1.2% GPLs weight fraction, the critical flutter aerodynamic pressure increases approximately 169%, 339% and 407%, respectively. It is also shown that the critical flutter aerodynamic pressure of a trapezoidal wing is more than that of the rectangular and skew wings having the same weight. The obtained numerical results of this research can be used as a suitable tool in analysis and design of wings of aeronautic vehicles at supersonic speeds.