Modeling and analysis of a resonant nanosystem
The majority of investigations into nanoelectromechanical resonators focus on a single area of the resonator's function. This focus varies from the development of a model for a beam's vibration, to the modeling of electrostatic forces, to a qualitative explanation of experimentally-obtained currents. Despite these efforts, there remains a gap between these works, and the level of sophistication needed to truly design nanoresonant systems for efficient commercial use. Towards this end, a comprehensive system model for both a nanobeam resonator and its related experimental setup is proposed. Furthermore, a simulation arrangement is suggested as a method for facilitating the study of the system-level behavior of these devices in a variety of cases that could not be easily obtained experimentally or analytically. The dynamics driving the nanoresonator's motion, as well as the electrical interactions influencing the forcing and output of the system, are modeled, experimentally validated, and studied. The model seeks to develop both a simple circuit representation of the nanoresonator, and to create a mathematical system that can be used to predict and interpret the observed behavior. Due to the assumptions used to simplify the model to a point of reasonable comprehension, the model is most accurate for small beam deflections near the first eigenmode of the beam. The process and results of an experimental investigation are documented, and compared with a circuit simulation modeling the full test system. The comparison qualitatively proves the functionality of the model, while a numerical analysis serves to validate the functionality and setup of the circuit simulation. The use of the simulation enables a much broader investigation of both the electrical behavior and the physical device's dynamics. It is used to complement an assessment of the tuning behavior of the system's linear natural frequency by demonstrating the tuning behavior of the full nonlinear response. The simulation is used to demonstrate the difficulties with the contemporary mixing approach to experimental data collection and to complete a variety of case studies investigating the use of the nanoresonator systems in practical applications, such as signal filtering. Many of these case studies would be difficult to complete analytically, but results are quickly achieved through the use of the simulation.
Rhoads, Purdue University.
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