We present an investigation of the nonlinear dynamics of clamped-clamped micromachined arches when actuated by a dc electrostatic load superimposed on an ac harmonic load. The Galerkin method is used to discretize the distributed-parameter model of a shallow arch to obtain a reduced-order model. The static response of the arch due to a dc load actuation is simulated, and the results are validated by comparing them to experimental data. The dynamic response of the arch to a combined dc load and ac harmonic load is studied when excited near its fundamental natural frequency, twice its fundamental natural frequency, and near other higher harmonic modes. The results show a variety of interesting nonlinear phenomena, such as hysteresis, softening behavior, dynamic snap-through, and dynamic pull-in. The results are also shown demonstrating the potential to use microelectromechanical systems (MEMS) arches as bandpass filters and low-powered switches. An experimental work is conducted to test arches realized of curved polysilicon microbeams when excited by dc and ac loads. Experimental data are shown for the softening behavior and the dynamic pull-in of the curved microbeams.

We present experimental and theoretical investigations of dynamic pull-in of electrostatically actuated resonators. Several experimental data are presented, showing regimes of ac forcing amplitude versus ac frequency, where a resonator is forced to pull in if operated within these regimes. Results are shown for primary and secondary resonance excitations. The influences of the initial conditions of the system, the ac excitation amplitude, the ac frequency, the excitation type, and the sweeping type are investigated. A shooting technique to find periodic motions and a basin-of-attraction analysis are used to predict the limits of the pull-in bands. When compared with the experimental data, the results have shown that the pull-in limits coincide with 30%-40% erosion lines of the safe basin in the case of primary resonance and 5%-15% erosion lines of the safe basin in the case of subharmonic resonance. Bifurcation diagrams have been constructed, which designers can use to establish factors of safety to reliably operate microelectromechanical-systems resonators away from pull-in bands and the danger of pull-in, depending on the expected disturbances and noise in the systems.

This study presents an effort to explore the exploitation of dynamic instabilities and bifurcations in micro-electro-mechanical systems to realize novel methods and functionalities for mass sensing and detection. These instabilities are induced by exciting a microstructure with a nonlinear forcing composed of a dc parallel-plate electrostatic load and an ac harmonic load. The frequency of the ac load is tuned to be near the fundamental natural frequency of the structure (primary resonance) or its multiples (subharmonic resonance). For each excitation method, local bifurcations, such as saddle-node and pitchfork, and global bifurcations, such as the escape phenomenon, may occur. This work aims to explore the utilization of these bifurcations to design novel mass sensors and switches of improved characteristics. One explored concept of a device is a switch triggered by mass threshold. The basic idea of this device is based on the phenomenon of escape from a potential well. This device has the potential of serving as a smart switch that combines the functions of two devices: a sensitive gas/mass sensor and an electromechanical switch. The switch can send a strong electrical signal as a sign of mass detection, which can be used to actuate an alarming system or to activate a defensive or a security system. A second type of explored devices is a mass sensor of amplified response. The basic principle of this device is based on the jump phenomena encountered in pitchfork bifurcations during mass detection. This leads to an amplified response of the excited structure making the sensor more sensitive and its signal easier to be measured. As case studies, these device concepts are first demonstrated by simulations on clamped-clamped and cantilever microbeams. Results are presented using long-time integration for the equations of motion of a reduced-order model. An experimental case study of a capacitive sensor is presented illustrating the proposed concepts. It is concluded that exciting a microstructure at twice its fundamental natural frequency produces the most promising results for mass sensing and detection.