  We characterize the dynamical states of a piezoelectric
microelectromechanical system (MEMS) using several numerical quantifers
including the maximal Lyapunov exponent, the Poincare Surface of Section and a
chaos detection method called the Smaller Alignment Index (SALI). The analysis
makes use of the MEMS Hamiltonian. We start our study by considering the case
of a conservative piezoelectric MEMS model and describe the behavior of some
representative phase space orbits of the system. We show that the dynamics of
the piezoelectric MEMS becomes considerably more complex as the natural
frequency of the system's mechanical part decreases.This refers to the
reduction of the stiffness of the piezoelectric transducer. Then, taking into
account the effects of damping and time dependent forces on the piezoelectric
MEMS, we derive the corresponding non-autonomous Hamiltonian and investigate
its dynamical behavior. We find that the non-conservative system exhibits a
rich dynamics, which is strongly influenced by the values of the parameters
that govern the piezoelectric MEMS energy gain and loss. Our results provide
further evidences of the ability of the SALI to efficiently characterize the
chaoticity of dynamical systems.
