Statics and dynamics of MEMS arches under axial forces

This works aims to investigate the effect of axial forces on the static behavior and the fundamental natural frequency of electrostatically actuated MEMS arches. The analysis is based on a nonlinear equation of motion of a shallow arch under axial and electrostatic forces. The static equation is solved using a reduced-order model based on the Galerkin procedure. The effects of the axial and electrostatic forces on the static response are examined. Then, the eigenvalue problem of the arch is solved for various equilibrium positions. Several results are shown for the variations of the natural frequency and equilibrium position of the arch under axial forces ranging from compressive loads beyond buckling to tensile loads and for voltage loads starting from small values to large values near the pull-in instability. It is found that the dynamics of MEMS arches are very sensitive to axial forces, which may be induced unintentionally through microfabrication processes or due to temperature variations while in use. On the other hand, it is shown that axial forces can be used deliberately to control the dynamics of MEMS arches to achieve desirable functions, such as extending their stable operation range and tuning their natural frequencies.