Use Simulink® to plot the angles i1(t) and i2(t) of the torsional MEMS shown in Fig. 7.45 of Problem 7.12. The flexible connectors are of circular cross section with a diameter d = 200 nm, a length l = 10 nm, and a shear modulus G = 0.8 # 1010 N/m2 . The rigid plates have a width w = 100 nm and thickness t = 5 nm. The material density is t = 3600 kg/m3 . The input torque is mt = 100 N-nm, and the initial conditions are zero.
Consider the torsional mechanical microsystem shown in Figure 7.45, formed of three identical flexible bars and two identical rigid plates. Derive the time domain mathematical model of this system and determine the transfer function matrix corresponding to the input t and the outputs i1 and i2. Confirm the obtained result by deriving the impedance-based transfer function matrix and the corresponding mechanical impedance circuit. Consider that known are the bars’ torsional stiffness k and the plates mass moment of inertia J.