Dynam ic Stability of a ShapeM emory Alloy Beam

A nonlinear dynamicsmodelwas derived based on the constitutive equations of the thermo- mechanical and pseudoelastic behaviors of shape memory alloy (SMA) and the dynamic equilibrium equations of an SMA beam. The analytic results show that the transverse vibration stability of the beam corresponds to the equilibriums of the phase transformations. At lower temperaturewheremartensite is stable, there are three fixed points: one representing stable center and the other two describing unstable saddle points. At themiddle temperature where bothmartensite and austenite coexis,t there are five fixed points: three representing stable centers and the other two describing unstable saddle points. Athigh temperaturewhere austenite is the exclusive stable phase, there is only one fixed point representing a stable cent