Resonators made from micro-/nanoelectromechanical systems are of great importance for their applications ranging from ultra-sensitive measurement to fundamental researches. In this work, we study the coupling between two mechanical modes in MEMS and NEMS resonators as well as the self-sustained oscillations that arises from the mode coupling. In the NEMS resonators made from MoS2 thin flakes, the internal resonance enables effective energy transfer between two modes and thus up-convert the input signals to its higher order harmonics. The dispersive coupling can act as a probe to detect the vibrations of mechanical modes that are hard to access. By parametrically modulating the mode coupling, the quality factors of the two modes are enhanced simultaneously and this provides an opportunity to improve the performance of such 2-dimension devices in room temperature. In the MEMS resonators, by pumping at the sideband of high frequency mode, additional linear or nonlinear friction force show up on the low frequency mode depending on the frequency of the modulation. The negative nonlinear friction leads to various of new phenomenon such as non-Lorentzian mode shape, energy-dependent dissipation and an isolated branch on top of normal driven response.

Self-sustained oscillations take place once the additional linear friction or negative nonlinear friction is strong enough to overcome the intrinsic energy dissipation. In the former case, self-sustained oscillations build up spontaneously by amplifying thermal fluctuations while in the latter case, zero amplitude is also stable and an excitation is required to activate the self-sustained oscillations. In both cases, the phase of two modes diffuses randomly and they add up to a constant due to the discrete time translation symmetry. The self-sustained oscillations can be used in signal transduction and frequency tuning element.