摘要
Electrostatic micromechanical actuators have numerous applicati ons in scie nee and technology.In many applications,they are operated in a narrow frequency range close to resonanee and at a drive voltage of low variation.Recently,new applications,such as microelectromechanical systems(MEMS)microspeakers(μSpeakers),have emerged that require operation over a wide frequency and dynamic range.Simulating the dynamic performance under such circumstances is still highly cumbersome.State-of-the-art finite element analysis struggles with pull-in instability and does not deliver the necessary in formation about un stable equilibrium states accordingly.Convincing lumped-parameter models amenable to direct physical interpretation are missing.This inhibits the in dispensable in-depth analysis of the dynamic stability of such systems.In this paper,we take a major step towards mending the situation.By combining the finite element method(FEM)with an arc-length solver,we obtain the full bifurcation diagram for electrostatic actuators based on prismatic Euler-Bernoulli beams.A subsequent modal analysis then shows that within very narrow error margins,it is exclusively the lowest Euler-Bernoulli eigenmode that dominates the beam physics over the entire relevant drive voltage range.An experiment directly recording the deflection profile of a MEMS microbeam is performed and confirms the numerical findings with astonishing precision.This enables modeling the system using a single spatial degree of freedom.
