Stability analysis of a parametrically excited functionally graded piezoelectric, MEM system

In this paper the mechanical behavior of a parametrically actuated functionally graded piezoelectric (FGP) clampedeclamped micro-beam is investigated. The micro-beam is supposed to be a composite material with silicon and piezoelectric base. The mechanical properties of the structure, including elasticity modulus, density, and piezoelectricity coefficient are supposed to vary along the height of the micro-beam with an exponential functionality. It is supposed that the FGP clampedeclamped microbeam is actuated with a combination of direct and alternative electric potential difference. Application of DC and AC actuation voltage leads in a constant and a time-varying axial force. The governing differential equation of the motion is derived using Hamiltonian principle and discretized using expansion theorem with the corresponding shape functions of a clampedeclamped beam. The discretized system is governed by Mathieu equation which¿s stability is investigated using Floquet theory for single degree of freedom systems and verified using multiple time scales of perturbation technique