Investigation of the dynamics of a clamped–clamped microbeam near symmetric higher order modes using partial electrodes

We present an investigation of the dynamics of a clamped–clamped microbeam excited electrostatically near its third and fifth natural frequencies. We study the effect of partial electrodes on the static and dynamic response of the beam. Different lower electrode configurations are utilized. A new concept of the divided lower electrode and its actuation with voltage sources of various phase shifts is introduced. A multi-mode Galerkin method is used to develop a reduced order model of the beam. Shooting and longtime integration methods are used to find the periodic motion and to generate frequency response curves. The curves show hardening behavior and dynamic pull-in. We show that the dynamic amplitude of the divided lower electrode, actuated with two voltage sources with phase shift, is higher than actuating the full electrode with one voltage source. These results are promising for the use of higher-order modes for mass detection and for ultra-sensitive resonant sensors.