Dynamic evolution of a primary resonance MEMS resonator under prebuckling pattern

Vibration Identification of Folded-MEMS Comb Drive Resonators

“…The later multiplication definitely increases the complexity of the governing equation. To balance the accuracy and simplicity of the theoretical solution, we successfully figured out an equation of motion similar to the above by the application of the MMS combined with the homotopy concept [ 25 ]. The residue theorem was used to find the secular terms in the system.…”

“…Therefore, the theoretical maximum vibration amplitude—in other words, dynamic pull-in amplitude—can be defined according to the distance between the non-zero unstable equilibrium and the zero stable equilibrium of the system. Obviously, dynamic pull-in vibration amplitude can be estimated as [ 24 , 25 ]: where , , , .…”

“…Although a relatively small DC voltage (far away from pull-in voltage) can yield consistent trends for their solutions compared with experiment results, when DC voltage is big enough, the theoretical results in Reference [ 7 ] may induce low prediction accuracy, which implies some of the limitations of their conclusions. What is more, based on our previous studies on a symmetric MEMS device, of which the governing equation of motion is very similar to this comb drive resonator, we successfully observed two primary frequency branches that existed in the system [ 25 ]. Perhaps, this dynamic MEMS device can also possess this property, which can be rationally utilized in enlarging the bandwidth and energy output for sensing and energy harvesting [ 25 ].…”

“…What is more, based on our previous studies on a symmetric MEMS device, of which the governing equation of motion is very similar to this comb drive resonator, we successfully observed two primary frequency branches that existed in the system [ 25 ]. Perhaps, this dynamic MEMS device can also possess this property, which can be rationally utilized in enlarging the bandwidth and energy output for sensing and energy harvesting [ 25 ]. In summary, all we want is to try to figure out two key problems of this folded-MEMS comb drive resonator.…”

“…In Section 2 , the governing equation of motion of a folded-MEMS comb drive resonator is introduced. In Section 3 , the MMS combined with the homotopy concept is applied to deduce the primary resonance solution [ 25 , 26 ]. A case study is carried out to reveal the existence of low and high-energy branches and intersection properties under primary resonance conditions.…”