Microelectromechanical (MEM) and Nanoelectromechanical (NEM) resonators represent a major class of MEM/NEM devices. Due to their nature of low damping and the presence of nonlinear potential fields, these devices are inherently nonlinear. From engineering point of view, to utilize the nonlinear behavior, it is critical to understand their dynamical mechanism as well as to design appropriate control scheme to operate the device in the desired nonlinear states. On the other hand, it is also necessary to devise schemes to prevent the undesired failure mode caused by nonlinear effects. In this work, the inherent nonlinear dynamical behaviors, methods for controlling nonlinear dynamics and techniques for mitigating mechanical shock are investigated in nonlinear MEM/NEM resonators. The specific applications explored within this work are electrostatically driven nanowire, coupled micro cantilever arrays and doubly clamped beam resonators.;For electrostatically driven nanowire, a detailed bifurcation analysis is carried out in a multiphysics model. One finding is that the nano-scale system can exhibit a vibration state with extremely strong chaotic characteristic. Potential applications of this vibration state are articulated.;For a micro cantilever resonator, the combination of mechanical nonlinearity and electrical driving force can lead to bistability. In this work, a robust control scheme based on analytic theory is proposed to place the system in the high-energy state.;For a microelectromechanical (MEM) resonator arrays, detailed analysis of a new mechanism of creating intrinsic localized modes (ILMs) is carried out in a typical experimental settings; that is, spatiotemporal chaos is ubiquitous and it provides a natural platform for actual realization of various ILMs through frequency control. In this type of device, a global control scheme to induce ILMs at arbitrary cantilever is proposed.;Performances of MEMS resonant devices can be seriously deteriorated when mechanical shocks interreact with devices' nonliearities. In this work, a scheme based on the idea of canceling common-mode disturbance by using symmetry is proposed to mitigate the shock effects on MEM devices. The performance degradations caused by mismatches of the device are predicted analytically.
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