Statics and Dynamics of V-Shaped Microbeams under Axial Forces

Hassen M. Ouakad, Nouha Alcheikh, Sofiane Ben Mbarek, Rodrigo Rocha, Mohammad I. Younis

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


This work proposes an examination into the static and dynamic behaviors of in-plane V-shaped microbeam under both electric forces and axial loads. The microbeams are actuated with two separate electrodes of uniform air gap across their length. The effects of the initial rise and DC bias voltage are examined while varying the axial loads ranging from compressive to tensile. The numerical analysis is based on a nonlinear equation of motion of a shallow V-shaped microbeam. The static and eigenvalue problem were solved using a modal expansion based reduced-order modeling for numerous equilibrium positions. The analytical model is validated by comparing to an experimental case study. The results show rich and diverse static and dynamic behavior. It is shown that the microbeam may exhibit only the pull-in or snap-through and pull-in instabilities. Various multistate and hysterics behaviors are demonstrated when varying the actuation forces and the initial rise. High tunability is demonstrated when varying the axial and DC loads for the first two symmetric vibration modes. With various axial load and DC actuation options and different geometrical configurations, this particular V-shaped microbeam shows a capacity of increasing the static deflection range before pull-in, allowing more variation of its fundamental natural frequency. Therefore, it could be more promising for the realization of different wide-range tunable microresonator as compared to the regular straight and even bell-shaped microbeams. These results are very useful in microscale applications that can be benefit for designing some structures with low power consumption, high sensitivity, and wide tuning range. Such rich behavior can be very useful for high-performance microscale applications designs.

Original languageBritish English
Article number091001
JournalJournal of Computational and Nonlinear Dynamics
Issue number9
StatePublished - 1 Sep 2021


  • axial forces
  • dynamic behavior
  • electrostatic actuation
  • pull-in and snapthrough instabilities
  • V-shaped micro-beam


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