Stochastic Response Analysis of Viscoelastic Shape Memory Alloy System

GUO Rong, LI Junlin, LIU Jiankang

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Journal of Shanxi University(Natural Science Edition) ›› 2025, Vol. 48 ›› Issue (3) : 435-444. DOI: 10.13451/j.sxu.ns.2023169
Mathematics and Applied Mathematics

Stochastic Response Analysis of Viscoelastic Shape Memory Alloy System

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Abstract

This article investigates the dynamic response of a viscoelastic shape memory alloy (SMA) spring oscillator system under narrow-band noise excitation. According to the constitutive relation of SMA polynomial, viscoelastic medium is introduced to describe spring damping, and the stochastic SMA dynamic equation is established. By using the method of combining Lindstedt-Poincaré and multi-scale, we get the amplitude-frequency response and steady-state moment equation of the system, and discuss the influence of viscoelastic parameters and noise intensity on the amplitude-frequency response and steady-state moment. The results show that the viscoelastic term can affect the nonlinear stiffness and structural damping of the system. Both noise intensity and viscoelastic parameters can induce random transition in the system. These results provide a theoretical reference for the stability of viscoelastic SMA composite structures.

Key words

narrow-band noise / shape memory alloy / multi-scale method / random transition

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GUO Rong , LI Junlin , LIU Jiankang. Stochastic Response Analysis of Viscoelastic Shape Memory Alloy System. Journal of Shanxi University(Natural Science Edition). 2025, 48(3): 435-444 https://doi.org/10.13451/j.sxu.ns.2023169

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