Ever since its inception, graphene has been the subject of research in many parts of the
world. This is due to its exceptional mechanical and electrical properties, which makes it
ideal for NanoElectroMechanical (NEMS) devices. The inherent nature of NEMS devices,
includes low damping, large amplitudes of oscillation, resonant operating conditions, and
the presence of nonlinear force fields. This sets an ideal stage for the appearance of nonlinear
behavior. In this thesis, appearance of such nonlinear behavior in optothermally actuated
graphene nanodrum resonators is studied. Frequency response arising from parametric
excitation is explained based on, time modulated stiffness due to temperature variation in
the membrane. Also, the response arising from direct excitation is discussed based on initial
geometric imperfection present in the membrane. In order to explain the nonlinear response
seen in graphene resonators, novel analytical models are developed and its corresponding
limitations are discussed. A single differential equation is used to simulate the behavior
of both directly and parametrically excited graphene nanoresonator. This equation is
used to study the influence of nonlinear damping on response of the system. Then, an
illustration is provided on characterization of graphene properties from the parametric
response of the system. Finally, it is concluded that, alternative damping mechanism and
other physical phenomena could be influencing the system dynamics. Therefore, modeling
of these phenomena would lead to better matching of the experimental results.