Rezaei, H., Kadkhodaei, M and Nahvi, H., 2012, Analysis of Nonlinear Free Vibration and Damping of a Clamped-Clamped Beam with Embedded Pre-strained Shape Memory Alloy Wires, Journal of Intelligent Material Systems and Structures, Vol 23, No 10, 1107-18

Nonlinear vibration and damping of a clamped-clamped composite beam containing shape memory alloy (SMA) wires embedded in the neutral surface are investigated. The constitutive relations of SMA are considered in the elastic response of the beam, and Hamilton’s principle is used to derive the differential equation of motion of the beam with extensible mid-plane. Considering mid-plane stretching in nonlinear analysis provides ability to model damping due to pseudoelasticity in the SMA wires where the wires experience tension. Although there is no distinct damping expression in the governing equation of motion, the results show gradual decrease in the free vibration amplitude of the beam until it reaches a fully elastic beam vibration. Free vibrations of the beam are evaluated, and phase diagrams, state of stress and strain, and variations of loss factor are studied. The results are also obtained for pre-strained SMA wires and their prominent influence on the vibration behavior of the beam is shown.