Analytical investigation of an energy harvesting shape memory alloy-piezoelectric beam

This work presents an analytical investigation of a cantilever shape memory alloy (SMA)/piezoelectric laminated composite beam subjected to a tip load with possible temperature variation. The beam consists of two piezoelectric layers of identical thickness bonded to a superelastic SMA core exhibiting asymmetric tensile-compressive behavior. Two loading scenarios are considered where either the temperature of the beam or the applied tip load is varied, while the other parameter is fixed. In each case, the load results in deformation of the SMA core and the piezoelectric layers bonded thereto, leading to the generation of an electric charge. The deformation of the SMA material is modeled based on an extended version of the ZM constitutive relations for SMAs that accounts for intrinsic tensile-compressive asymmetry. Geometric and force equilibrium considerations are used to identify the correct sequence in which different solid-phase structures develop within the superelastic core during a complete loading-unloading process. Temperature-dependent moment and shear force equations are then derived and used in investigating the electrical and mechanical properties of the beam. The proposed model is validated against 3D finite element simulations, and the general trend of output voltage variation with temperature is shown to be consistent with experimental data.