Problems associated with the modeling and vibration control of rectangular plates under dynamic loads with integrated polycrystalline NiTi shape memory alloy (SMA) ribbons are developed. In order to simulate the thermo-mechanical behavior of SMA ribbons under dominant axial and transverse shear stresses, a robust macroscopic constitutive model is introduced. The model is able to accurately predict martensite transformation/orientation, shape memory effect, pseudo-elasticity and in particular reorientation of martensite variants and ferro-elasticity features. The structural model is based on the adoption of the first-order shear deformation theory and on the geometrical non-linearity in the von Kármán sense. Towards obtaining the governing equations of motion, the Hamilton principle is used. Finite element and Newmark methods along with an iterative incremental process based on the elastic-predictor inelastic-corrector return mapping algorithm are implemented to solve the non-linear governing equations in spatial and time domains. Numerical simulations highlighting the implications of pre-strain state and temperature of the SMA ribbons, as well as those related to the respective dynamic loads, are presented and discussed in detail. It is found that the modeling of ferro-elasticity in the dynamic analysis of SMA composite structures could lead to significant conclusions concerning the passive vibration control capability of low-temperature SMA ribbons.
Shape memory elastic foundation and supports for passive vibration control of composite plates
