Hysteretic modeling of shape memory alloy vibration reduction devices

Shape Memory Materials (SMM) are widely used in various engineering fields for several applications including actuators, composites, servomechanisms among the others. A further application field is offered by the exploitation of the pseudoelastic effect (hysteresis without residual displacements at unloading) for the reduction of the vibrations. To this end, various SMM elements are arranged to give rise to a device that produces the desired behavior. In other cases the vibration reduction devices may be obtained from the combination of SMM and non-SMM elements, likely elastoplastic, to increase the amount of energy dissipation. While all models for SMM refer to the behavior of the material alone, in this work the attention is focused on the device-level and a suitable framework is proposed to deal with the above mentioned applications. The proposed model for SMM is based on the rate-independent hysteresis algorithm formulated by Ivshin and Pence. Proper modifications aimed to the modeling of the vibration devices are introduced. The model belongs to the class of Duhem hysteresis models in the sense of Visintin and it is embedded in a thermomechanical framework that enables to quantitatively describe the SMM response under arbitrary loading paths including internal subloops and the dependence of the hysteresis loop shape on the temperature. The analysis of the dynamic stationary response of the device under harmonic forcing excitation is presented through excitation frequency-response amplitude curves.