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On the nonlinear resonances and dynamic pull-inof electrostatically actuated resonators

In this project, the students will apply the concept of lumped parameter modeling they learn in the classes to investigate the dynamic behavior of the electrostatic resonator. Toward this, the unknown elements of the lumped parameter modeling need to be estimated using the methods and techniques we learned in Chapter 4. After that, you need to start investigating the dynamic behavior of the electrostatic resonator by applying the fundamental concepts in nonlinear dynamics discussed in Chapter 5. Such concepts include nondimensionalization of the equation of motion, finding the equilibrium points of the dynamical system and analyzing their stability, analyzing the static and dynamics bifurcations at the equilibrium points, and sketching the phase portrait of the system for multiple cases below and beyond the pull-in voltage. Finally, you are required to analyze the dynamic behavior around the resonance frequency regime by plotting the frequency response curves at different excitation voltages (Vdc, Vac). For this part, Shooting Technique (Chapter 7) is required to be used to catch the periodic solutions as well as both stable and unstable solutions.