期刊
MICROSYSTEMS & NANOENGINEERING
卷 7, 期 1, 页码 -出版社
SPRINGERNATURE
DOI: 10.1038/s41378-021-00265-y
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资金
- Fraunhofer Zukunftsstiftung
- State of Brandenburg
- European Union [80256335]
This study successfully analyzes the dynamic performance of electrostatic actuators based on Euler-Bernoulli beams by combining the finite element method with an arc-length solver. Experimental results closely match the numerical findings, confirming that the lowest Euler-Bernoulli eigenmode dominates the beam physics over the entire drive voltage range.
Electrostatic micromechanical actuators have numerous applications in science and technology. In many applications, they are operated in a narrow frequency range close to resonance and at a drive voltage of low variation. Recently, new applications, such as microelectromechanical systems (MEMS) microspeakers (mu Speakers), 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 information about unstable equilibrium states accordingly. Convincing lumped-parameter models amenable to direct physical interpretation are missing. This inhibits the indispensable 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.
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