抄録
In this paper, the nonlinear vibration behavior of a composite beam with embedded shape memory alloy (SMA) wires is investigated. The wires are embedded in the neutral surface of the beam. Using a variational formulation, the governing equations of motion and associated boundary conditions for the beam with extensible mid-plane are obtained. Considering mid-plane stretching in nonlinear analysis provides several unique advantages that cannot be obtained in linear analysis. It allows modeling damping due to pseudo-elasticity property of wires and the effect of vibration amplitude and initial conditions on the beam vibration characteristics. In this study, the constitutive relations of SMA are combined with elastic properties of the beam to derive governing differential equation of motion. Although there is no distinct damping term in the governing equation, the results show decrease in the vibration amplitude. Corresponding phase plane diagrams, as well as, the stress-strain curves for the SMA are obtained. The variation of damping with strain amplitude for different initial conditions is studied and the general features of the responses are found to be in agreement with the reported experimental observations.
