Stochastic static behaviors and dynamic responses of penta-graphene plates

In this study, nonlinear bending, buckling, free- and forced vibrations of thin penta-graphene plates resting on elastic foundations were investigated in deterministic and stochastic environments. The thin plates undergo small strain conditions described by the classical plate theory and extended Hamilton principles. The Bubnov-Galerkin method and fourth-order Runge-Kutta methods were applied for explicit closed-form solutions of nonlinear static and dynamic behaviors of penta-graphene plates considering geometry imperfection. Effects of elastic foundations, geometry imperfection, and excitation amplitudes and frequencies on deterministic bending, buckling, and vibration of penta-graphene plates were examined. For analyzing the plate in stochastic environments, randomness of material properties, geometry, and elastic bases were sampled using Monte Carlo simulations. Stochastic bending, buckling, and vibration analysis of penta-graphene plates were performed using theoretical solutions and statistical methods. Geometry ratios of penta-graphene plates have strong effects on their stochastic bending behaviors, elastic foundations have strong effects on stochastic buckling behaviors, while both geometry ratios and vibration amplitudes show strong effects on the backbone and forced-response curves of penta-graphene plates.