Dynamic Instability of Functionally Graded Graphene Platelet-Reinforced Porous Beams on an Elastic Foundation in a Thermal Environment

Under thermal environment and axial forces, the dynamic instability of functionally graded graphene platelet (GPLs)-reinforced porous beams on an elastic foundation is investigated. Three modes of porosity distributions and GPL patterns are considered. The governing equations are given by the Hamilton principle. On the basis of the differential quadrature method (DQM), the governing equations are changed into Mathieu–Hill equations, and the main unstable regions of the porous composite beams are studied by the Bolotin method. Thermal buckling and thermo-mechanical vibration problems are also studied. The effects of porosity coefficients and GPL weight fraction, dispersion pattern, initial thermal loading, slenderness ratio, geometry and size, boundary conditions, and foundation stiffness are discussed. The conclusions show that an elastic foundation has an obvious enhancement effect on thermal buckling, free vibration, and dynamic instability, which improves the stiffness of the beam.