In-plane dynamic instability of functionally graded porous arches reinforced by graphene platelet under a vertical base excitation

The in-plane dynamic instability of functionally graded porous (FGP) circular arches made of graphene platelets reinforced composites (GPLRC) under a vertical base excitation is investigated in this paper. The elastic modulus and mass density of the arch are predicated according to Halpin-Tsai micromechanics model and rule of mixture, respectively. The equilibrium differential equations for dynamic stability of the arch are derived based on Hamilton's principle. Dynamic unstable regions corresponding to period T and period 2T are determined by using Bolotin method. A comprehensive parametric study is then carried out, with a particular focus on the effects of porosity distribution, porosity coefficient, GPL weight fraction and geometry size, and damping ratios on the parametric resonance and the resonance behavior of the FGP-GPLRC arch. The results indicate that the GPL arch with symmetric porosity distribution has the narrowest unstable region in both periods, followed by the asymmetric and uniform distributions. It is also found that a stronger vertical base excitation is required to trigger the dynamic instability for the FGP-GPLRC arch with a larger damping ratio.