黏弹形状记忆合金系统的随机响应分析

郭蓉, 李俊林, 刘健康

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山西大学学报(自然科学版) ›› 2025, Vol. 48 ›› Issue (3) : 435-444. DOI: 10.13451/j.sxu.ns.2023169
基础数学与应用数学

黏弹形状记忆合金系统的随机响应分析

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Stochastic Response Analysis of Viscoelastic Shape Memory Alloy System

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摘要

本文研究了窄带噪声激励下黏弹形状记忆合金（Shape Memory Alloy， SMA）弹簧振子系统的动力学响应。根据SMA多项式本构关系，引入黏弹性介质描述弹簧阻尼，建立了随机SMA动力学方程。采用Lindstedt-Poincaré和多尺度相结合方法，得到系统的幅频响应和稳态矩方程，并探讨了幅频响应与稳态矩随黏弹参数、噪声强度等变化的规律。研究结果表明，黏弹项能够影响系统的非线性刚度和结构阻尼；噪声强度和黏弹参数都能够诱导系统发生随机跃迁现象。这些都为黏弹SMA复合结构的稳定性提供了理论参考。

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.

关键词

窄带噪声 / 形状记忆合金 / 多尺度法 / 随机跃迁

Key words

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

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O193

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郭蓉 , 李俊林 , 刘健康. 黏弹形状记忆合金系统的随机响应分析. 山西大学学报(自然科学版). 2025, 48(3): 435-444 https://doi.org/10.13451/j.sxu.ns.2023169
GUO Rong, LI Junlin, LIU Jiankang. Stochastic Response Analysis of Viscoelastic Shape Memory Alloy System[J]. 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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山西省高等学校科技创新项目(2022L316)

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