On the free vibration of thermally pre/post-buckled shear deformable SMA hybrid composite beams

The objective of this article is to analytically investigate the free vibration of shape memory alloy hybrid composite (SMAHC) beams in thermally pre/post-buckled domains. Non-linear equations of motion of SMAHC beams are derived based on the first-order shear deformation theory and von Karman geometrical non-linearity via the extended Hamilton principle. The recovery stress generated by temperature-induced martensitic phase transformation of the pre-strained SMA fibers is computed by means of the Brinson model. Exact closed-form solutions are presented for the buckling temperature, post-buckling deformation and temperature-deformation equilibrium path of symmetric and asymmetric simply supported SMAHC beams under uniform temperature rise. The vibration of the symmetric SMAHC beam around the first buckled configuration is also investigated and an analytical solution for the fundamental frequency and its associated mode shape is obtained. Based on the developed closed-form solutions, extensive numerical results are presented to provide an insight into the influence of SMA fibers volume fraction, pre-strain in the SMA fibers, location of SMA fibers, temperature rise and geometrical parameters on the static and dynamic responses of the SMAHC beams in the thermally pre/post-buckling regimes. Due to the absence of similar results in the specialized literature, this paper is likely to fill a gap in the state of the art of this problem.