  Bifurcation analysis of dynamic pull-in for a lumped mass model is presented.
The restoring force of the spring is derived based on the nonlinear
constitutive stress-strain law and the driving force of the mass attached to
the spring is based on the electrostatic Coulomb force, respectively. The
analysis is performed on the resulting nonlinear spring-mass equation with
initial conditions. The necessary and sufficient conditions for the existence
of periodic solutions are derived analytically and illustrated numerically. The
conditions for bifurcation points on the parameters associated with the
second-order elastic stiffness constant and the voltage are determined.

Dynamical Systems