Direct Stochastic Equivalent Linearization of Sdof Smart Mechanical System

The first and second moments of response variables for SDOF system with pseudoelastic material are obtained by a direct linearization procedure. This procedure is an adaptation of well-known statistical linearization methods, and 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. This implementation eliminates the effort of deriving linearization coefficients for new SMA hysteresis model. In this paper the complete statistical response of SDOF system containing a mass and a bar made of SMA is obtained via direct linearization procedure. The model considered is modification of 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 shape memory alloys. Response statistics for zero mean random vibration are obtained. Furthermore, non-zero mean analysis of the system is carried out and comparisons are made with Monte Carlo simulation.