ASME International Mechanical Engineering Congress and Exposition

We developed a distributed-parameter model (partial differ-ential equations and associated boundary conditions) that de-scribe the coupled torsion and bending motions of the Digital Micromirror Device (DMD) using the extended Hamilton prin-ciple. The work done by the electrostatic field is expressed in the form of a potential energy. It is found that coupling between the torsion and bending motions appears in the boundary con-ditions. The nonlinearity is mainly due to the application of the electrostatic forces and moments. Nonlinear terms appear only in the boundary conditions. The developed model provides a basis for a thorough study of the static and dynamic behaviors of the electromechanical device. The static response of the DMD for different DC loads shows the occurrence of pull-in (snap-down) instability at critical voltage values corresponding to the collapse of the yoke to mechanical stops. Estimates of the voltage, an-gle, and deflection at pull-in are given. The dynamic behavior of the DMD is analyzed by plotting the natural frequencies versus the applied DC voltage. We conducted a study of the sensitivity of the static and dynamic behaviors of the micromirror to vari-ations in the geometric parameters of the DMD. It is found that the thickness and width of the hinges are the key parameters in-∗Address all correspondence to this author