 
Summary: Usequence in electrostatic
microelectromechanical systems (MEMS)
BY SUDIPTO K. DE AND N. R. ALURU*
Department of Mechanical and Industrial Engineering,
Beckman Institute for Advanced Science and Technology,
University of Illinois at UrbanaChampaign, Urbana IL 61801, USA
In this paper, the presence of U(Universal)sequence (a sequence of periodic windows
that appear beyond the period doubling (PD) route to chaos) in electrostatic
microelectromechanical systems (MEMS) is reported. The MEM system is first brought
to a nonlinear steady state by the application of a large dc bias close to the dynamic pull
in voltage of the device. An ac voltage (the bifurcation parameter) is next applied to the
system and increased gradually. A sequence of PD bifurcations leading to chaos is
observed for resonant and superharmonic excitations (frequency of the ac voltage). On
further increase in the ac voltage (beyond where chaos sets in), Usequence is observed in
the system. Under superharmonic excitation, the sequence is found to be a modified form
of the Usequence referred to as the `UMsequence' in this paper. The appearance of a
periodic window with K oscillations per period or Kcycles in the normal Usequence
is replaced by a corresponding periodic window with KMcycles in the UMsequence.
M stands for the Mth superharmonic frequency of excitation. The formation of the
periodic windows from a chaotic state in the UMsequence takes place through
