Mathematical Model of a Shape Memory Alloy Spring Intended for Vibration Reduction Systems

Abstract

The article discusses a prototype of a Shape Memory Alloy (SMA) spring intended for controlled vibration reduction systems. The spring has been subject to experiments and the article presents selected static and dynamic characteristics. The experiments were conducted at the Dynamics and Control of Structures Laboratory of the AGH University of Science and Technology. They permitted the formulation of a mathematical model for the SMA spring. The model takes into account the phenomena of energy accumulation and dissipation. The parameters of the spring model have been determined, based on the experimental data. The model takes into account the relationship of stiffness and damping to alloy temperature and the frequency of excitation. It has been demonstrated that the properties of the spring may be altered under controlled conditions. The spring model was then used in simulations. They served as the basis for the determination of the frequency response characteristics, which were then compared to the characteristics of a real spring. The mathematical model developed may be applied in the design of passive, semi-active, and active vibration reduction systems, as well as in the synthesis of adaptive smart vibration reduction systems.