Dynamic instability of functionally graded porous arches reinforced by graphene platelets

This paper investigates the dynamic instability of a functionally graded porous arch reinforced with uniformly distributed graphene platelets (GPLs) under the combined action of a static force and a dynamic uniform pressure in the radial direction. The relationship between the elastic modulus and mass density of the material is determined by the closed-cell cellular solids under Gaussian Random Field scheme. The governing equation is derived based on classical Euler-Bernoulli theory. Galerkin approach is used to derive the Mathieu-Hill equation from which the dynamic unstable region is obtained using Bolotin method. A comprehensive parametric study is conducted to examine the effects of GPL weight fraction and dimensions, porosity distribution, pore size, static force, and arch geometry and size on the dynamic stability characteristics of the arch. Numerical results show that the porous arch's resistance against dynamic instability can be considerably improved by using symmetrically non-uniform porosity distribution and the addition of a small amount of GPLs.