Out-of-plane dynamic instability of functionally graded porous circular arches reinforced by graphene platelets in thermal environment

This paper investigates out-of-plane dynamic instability for functionally graded porous (FGP) graphene platelets reinforced composites (GPLRC) circular shallow arches subjected to a radial periodic concentrated load in a thermal environment for the first time. Hamilton principle is employed to derive the differential equations of motion of the arches associated with out-of-plane displacements. The dynamic instability regions (DIR) with period 2T are determined by using Bolotin’s method and verified by finite element software ANSYS. The effects of uniform temperature difference,out-of-plane boundary condition, pore distribution mode, the weight fraction of graphene platelets (GPLs), GPLs dimension coefficients, and the location of the concentrated periodic load on the DIRs are comprehensively analyzed. The results show that higher temperature difference can weaken the dynamic stability of the arch. The load position has no influence on the boundary excitation frequency at the lowest point of the DIR but plays a negative impact on the area of the DIRs and a positive influence on the lowest value of the load. The parametric resonance of the arch is more likely to occur if the concentrated periodic load is located near the arch crown.