Microsystems & Nanoengineering (May 2021)

Coulomb-actuated microbeams revisited: experimental and numerical modal decomposition of the saddle-node bifurcation

  • Anton Melnikov,
  • Hermann A. G. Schenk,
  • Jorge M. Monsalve,
  • Franziska Wall,
  • Michael Stolz,
  • Andreas Mrosk,
  • Sergiu Langa,
  • Bert Kaiser

DOI
https://doi.org/10.1038/s41378-021-00265-y
Journal volume & issue
Vol. 7, no. 1
pp. 1 – 13

Abstract

Read online

Abstract 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 (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 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.