Analysis of nonlinear free vibration and damping of a clamped–clamped beam with embedded prestrained shape memory alloy wires

Nonlinear free vibration and damping of a clamped–clamped composite beam containing shape memory alloy wires with different prestrains embedded in the midsurface are investigated. The constitutive relations of shape memory alloy are considered in the large deflection response of the elastic Euler–Bernoulli beam, and Hamilton’s principle is used to derive differential equation of the beam motion with extensible midplane. Considering midplane stretching due to tension in the shape memory alloy wires provides an ability to model damping in a nonlinear analysis although there is no distinct damping expression in the governing equation of motion. The results show a gradual decrease in the free vibration amplitude of the beam until it reaches a fully elastic response while this cannot be seen in linear models. Free vibrations of the beam are investigated, and time response, phase diagram, state of stress and strain in the wires, and variations of loss factor are studied. The effect of prestrain in the shape memory alloy wires on the final stable vibration amplitude and loss factor in free vibrations of the beam is also investigated.