Postprint version. Published in Proceedings of the 8th ASCE Specialty Conference on Probabilistic Mechanics and Structural Reliability: South Bend, Indiana, July 22, 2000. 6 pages. ©American Society of Civil Engineers.
At the time of publication, the author Mohammad N.Noori was affiliated with North Carolina State University. Currently, August 2008, he is the Dean of the College of Engineering at California Polytechnic State University - San Luis Obispo.
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.