Damping capacity in pseudo-elastic and ferro-elastic shape memory alloy-reinforced hybrid composite beam

Abstract

Reinforcing a composite beam with shape memory alloy wires may have several benefits such as reduction of buckling risks or elimination of unwanted oscillations. In this paper, the vibration damping of a typical shape memory alloy-reinforced composite or hybrid beam is explored. To formulate the thermo-mechanical behavior of embedded shape memory alloy wires, three-dimensional Panico–Brinson model is employed and tailored to one-dimensional model. This material model can simulate pseudo-elastic and ferro-elastic forms of martensite transformations which occurs in cyclic loadings. Besides, unlike the former studies which rely on classical beam theories, the first-order shear deformation beam theory is used to obtain more accurate estimations of shape memory alloy-wire hysteresis loops and their decaying characteristics. In order to explore the effects of a transient concentrated load applied in the middle of a beam, the governing equations are developed and discretized by differential quadrature–integral quadrature combined method. Incremental time marching solution of the problem is accomplished using the Newmark technique. Results are assessed by comparing with available literature. Considering different types of boundary conditions, the influence of pseudo-elastic and ferro-elastic hysteresis loops on the material damping effects, shape memory alloy volume fraction, and resonance phenomenon is studied in detail.