The present contribution deals with developing a semi-analytical analysis for studying the free vibration of a shape memory alloy beam with pseudoelastic behavior. The equations of motion are derived using the Hamilton principle and the Euler–Bernoulli theory. Then mathematical processes of non-dimensionalization and numerical integration are performed and finally the obtained partial differential equations are solved using the Galerkin method. A three-dimensional phenomenological model for shape memory alloy, which has the capability of identifying the martensite phase transformation, saturated phase transformation, pseudoelasticity and the shape memory effect, is utilized for modeling the shape memory alloy. According to the hysteresis behavior of the shape memory alloy, the energy dissipation characteristic is clearly observed in the early stages of the free vibration. Stress and strain analysis is employed to specify the effect of phase transformation in each layer along the beam. The property of shape memory alloy beam demonstrates its great potential for using in damping applications.

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