Nonlinear Equilibrium Paths of a Microbeam subjected to an Electrostatic Force Field
The objective of this project was to describe the nonlinear equilibrium paths of a microbeam under electrostatic forces. Such structure is in the micro scale, and is therefore considered a micro electro mechanical system (MEMS). The microbeam was described by nonlinear equations of motion, and the electrostatic force field by a fully nonlinear model. The plot below shows the diagram of the microbeam model, with the actuator which induces the electrostatic force field.
The discretization of the beam was based on Galerkin’s method. A single-degree-of-freedom system was also used whereby the electrostatic force could be represented over its full displacement range. The plot below shows a mid-span displacement vs load graph. As can be observed, the beam stiffness increases up to an inflection point, subsequently decreasing until it becomes unstable (dashed line). Physically, after the critical point the beam has a tendency to snap through towards the actuator. In order to recover the nonlinear unstable region, a path-following algorithm has been developed and implemented.
This structure can be used as a mechanical vibration/acoustic emission sensor (e.g. accelerometers, pressure, strain, vibration and temperature sensors) and is especially attractive for aerospace applications. The results of this project are reported in Section 1.6.2 of my supervisor’s book, Walter Lacarbonara Nonlinear Structural Mechanics.
