Gilberto Flores

ANALYSIS OF THE DYNAMICS AND TOUCHDOWN IN A MODEL OF ELECTROSTATIC MEMS

We study a reaction‐diffusion equation in a bounded domain in the plane, which is a mathematical model of an idealized electrostatically actuated microelectromechanical system (MEMS). A relevant feature in these systems is the “pull‐in” or “jump‐to contact” instability, which arises when applied voltages are increased beyond a critical value. In this situation, there is no longer a steady state configuration of the device where mechanical members of the device remain separate. It may present a limitation on the stable operation regime, as with a micropump, or it may be used to create contact, as with a microvalve. The applied voltage appears in the equation as a parameter. We prove that this parameter controls the dynamics in the sense that before a critical value the solution evolves to a steady state configuration, while for larger values of the parameter, the “pull‐in” instability or “touchdown” appears. We estimate the touchdown time. In one dimension, we prove that the touchdown is self‐similar and d...

Dynamics and Touchdown in Electrostatic MEMS

Perhaps the most widely known nonlinear phenomena in nano- and microelectromechanical systems is the “pull-in” or “jump-to-contact” instability. In this instability, when applied voltages are increased beyond a certain critical voltage there is no longer a steady-state configuration of the device where mechanical members remain separate. This instability affects the design of many devices. It may present a limitation on the stable range of operation, as with a micropump, or may be utilized to create contact, as with a microvalve. Here, a mathematical model of an idealized electrostatically actuated MEMS or NEMS device is constructed for the purpose of studying the dynamics and touchdown behavior of systems operated in the pull-in regime. The model is analyzed in the viscosity dominated limit. This gives rise to a non-linear parabolic equation of reaction-diffusion type. The model is studied using a combination of analytical and numerical techniques.Copyright