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We characterize the dynamical states of a piezoelectricmicroelectromechanical system (MEMS) using several numerical quantifersincluding the maximal Lyapunov exponent, the Poincare Surface of Section and achaos detection method called the Smaller Alignment Index (SALI). The analysismakes use of the MEMS Hamiltonian. We start our study by considering the caseof a conservative piezoelectric MEMS model and describe the behavior of somerepresentative phase space orbits of the system. We show that the dynamics ofthe piezoelectric MEMS becomes considerably more complex as the naturalfrequency of the system's mechanical part decreases.This refers to thereduction of the stiffness of the piezoelectric transducer. Then, taking intoaccount the effects of damping and time dependent forces on the piezoelectricMEMS, we derive the corresponding non-autonomous Hamiltonian and investigateits dynamical behavior. We find that the non-conservative system exhibits arich dynamics, which is strongly influenced by the values of the parametersthat govern the piezoelectric MEMS energy gain and loss. Our results providefurther evidences of the ability of the SALI to efficiently characterize thechaoticity of dynamical systems.

Chaotic dynamics of piezoelectric mems based on maximal Lyapunov exponent and Smaller Alignment Index computations