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

Luis D. Duval; Mohammad N. Noori; Zhikun Hou; Hamid Davoodi

doi:10.1117/12.388780

19 June 2000 Direct stochastic linearization of a mechanical system with pseudoelastic shape memory alloy

Luis D. Duval, Mohammad N. Noori, Zhikun Hou, Hamid Davoodi

Proceedings Volume 3984, Smart Structures and Materials 2000: Mathematics and Control in Smart Structures; (2000) https://doi.org/10.1117/12.388780
Event: SPIE's 7th Annual International Symposium on Smart Structures and Materials, 2000, Newport Beach, CA, United States

Abstract

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.

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Luis D. Duval, Mohammad N. Noori, Zhikun Hou, and Hamid Davoodi "Direct stochastic linearization of a mechanical system with pseudoelastic shape memory alloy", Proc. SPIE 3984, Smart Structures and Materials 2000: Mathematics and Control in Smart Structures, (19 June 2000); https://doi.org/10.1117/12.388780

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KEYWORDS

Shape memory alloys

Systems modeling

Complex systems

Stochastic processes

Cerium

Mathematical modeling

Statistical analysis

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