Random vibration of SMA systems via Preisach formalism

Interest in shape memory alloys (SMA) applications has increased dramatically in recent years. The primary problem in studying systems endowed with SMA devices involves quantifying their mechanical behaviour. A most promising tool for this task is the Preisach model, which, due to its abstract nature, is extremely versatile for capturing various hysteretic phenomena present in SMA. In this paper a procedure to calibrate the Preisach model to fit available experimental data is employed first. Then the random responses of SMA systems are investigated by focusing on the numerical implementation of the Preisach model. A version of the stochastic averaging technique is used for this purpose. The probability density function of the amplitude and the power spectral density of the response are determined. Also, the probability density function of the response process is estimated. The analytical results are found in good agreement with those derived by a pertinent Monte Carlo study. Obviously, the methodology described herein can be applied for the study of other hysteretic systems, such as mechanical joints, provided, that adequate calibration of the Preisach model has been performed a priori.