We applied the finite element method to simulate and predict the vibrational response of graphene sheets in order to obtain the eigenfrequencies and their corresponding eigenmodes under different boundary conditions. Furthermore, various types of topological defects (i.e., carbon vacancies, Stone-Wales defect, and perturbation) and functionalization modifications (i.e., chemical doping) are introduced to the structure of the model in order to realistically predict the vibrational behavior of those nanoparticles in a closer form to those found in reality. Computational results indicate that both topological and chemical imperfections result in significant changes in the vibrational response of the nanosheet and considerable reduction in the natural frequencies of the model and as a consequence, reducing the vibrational stability of these nanostructures.