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Nanoelectromechanical systems (NEMS) have drawn considerable attention towards several sensing applications such as force, spin, charge and mass. Due to their smaller size, these devices operate at very high frequencies and have very high quality factors. However, several nonlinearities present in the system affect the performances of these miniscule devices. In this work, we investigate the effect of geometric imperfections on the performances of graphene based NEMS. The electromechanical properties of the doubly clamped graphene resonators deviate from the flat rectangular plate as the former possesse ripples and wrinkles that are sometimes orders of magnitude larger than the thickness of the resonator. Apart from these, fabrication process also introduces imperfection in the graphene sheet. Due to aforementioned imperfections, the nonlinear properties of graphene resonator vary from their readily observed entirely hardening or entirely softening behavior. In this work, we report an initial weak softening behavior for graphene resonators for small vibration amplitudes. However, for large vibration amplitudes, the device shows strong hardening behavior. The initial softening behavior can be explained by incorporating the effect of geometric imperfection in quadratic nonlinearity. We have used the harmonic balance method coupled with the asymptotic numerical method to obtain theoretically the periodic solutions, which are in good agreement with the experimental results.