Direct stochastic linearization of a mechanical system with pseudoelastic shape memory alloy

The first and second moments of response variables for SDOF system with pseudoelastic SMA's are obtained by a direct linearization procedure. This is an adaptation in the implementation of well-known statistical linearization methods, which provides concise, model-independent linearization coefficients. The method can be applied to systems that incorporate any SMA hysteresis model having a differential constitutive equation and can be used for zero and non-zero mean random vibration. The implementation eliminates the effort of deriving linearization coefficients for new SMA hysteresis model. In this work the statistical response of SDOF system containing a mass and a bar made of SMA is obtained via direct linearization procedure. The model considered is a phenomenological one-dimensional constitutive model, originally proposed by Graesser and Cozzarelli, which provides the capability to model both the martensitic twinning hysteresis and martensitic-austenite pseudoelastic behavior typical of SMA's. Response statistics for zero mean random vibration can be obtained. Furthermore, non-zero mean analysis of the system is carried out and comparisons are made with Monte Carlo simulation.