The aim of this research is to introduce a semi-analytical approach for the analysis of the free and forced nonlinear vibrations of a bending shape memory alloy (SMA) beam; while, considering the effect of its pseudo-elastic behavior. In order to create a primary deflection, an appropriate pre-strain is applied to the SMA beam using a compression spring. A new material model was utilized to simulate the nonlinear hysteric behavior of the SMA beam, while the differential equations of motion of the beam were derived based on Euler–Bernoulli beam theory and Hamilton principle. The extracted nonlinear partial differential equations of motion are semi-analytically solved by utilizing the Galerkin method. The pseudo-elastic behavior and energy dissipation of the SMA beam were studied in the free and forced nonlinear vibration regimes. Finally, the influences of the system parameters such as the spring constant, amplitude, and frequency of the excitation force on the absorber efficiency were investigated, and its stability was studied. The numerical results depict that the SMA beam exhibits a highly nonlinear dynamical behavior, and can be used as an actuator for energy dissipation.

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