| 非对称碰撞约束下形状记忆合金梁的随机响应与分岔 |
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| 引用本文： | 李玉婷,冯进钤.非对称碰撞约束下形状记忆合金梁的随机响应与分岔[J].数学研究及应用,2022,42(5):539-550. |
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| 作者姓名： | 李玉婷 冯进钤 |
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| 作者单位： | 吉林大学数学学院, 吉林 长春130012;西安工程大学理学院, 陕西 西安710048 |
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| 基金项目： | 陕西省自然科学基金(Grant No.2018JM1044). |
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| 摘 要： | 形状记忆合金(SMA)是二十一世纪具有形状记忆效应的新型智能材料.针对具有非对称约束的SMA梁,本文构造了碰撞振动系统.在无碰撞和有碰撞两种情况下,利用随机平均法给出了近似解析结果.数值模拟作为验证解析结果的工具.结果表明,系统能量的概率响应曲线具有非光滑特性.当约束位置发生变化时,系统会出现随机P分岔和D分岔.
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| 关 键 词： | 形状记忆合金 随机平均 概率密度函数 随机P分岔 随机D分岔 |
| 收稿时间： | 2022/4/24 0:00:00 |
| 修稿时间： | 2022/5/22 0:00:00 |
Stochastic Responses and Bifurcations of Shape Memory Alloy Beam under Asymmetric Impacting Constraint |
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| Yuting LI,Jinqian FENG.Stochastic Responses and Bifurcations of Shape Memory Alloy Beam under Asymmetric Impacting Constraint[J].Journal of Mathematical Research with Applications,2022,42(5):539-550. |
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| Authors: | Yuting LI Jinqian FENG |
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| Institution: | College of Mathematics, Jilin University, Jilin 130012, P. R. China; College of Science, Xi''an Polytechnic University, Shaanxi 710048, P. R. China |
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| Abstract: | Shape Memory Alloy (SMA) is a new type of smart material with shape memory effect in the 21st century. In this work, the vibro-impact (VI) system is constructed for an SMA beam with asymmetric constraint. In two cases of non-impacting and impacting for Hamiltonian function, the approximate analytical results are presented by taking advantage of the stochastic averaging method. Numerical simulation emerges as the tool that verifies the obtained analytical results. In particular, the discussed results reveal that the probability response curve of the system energy demonstrates non-smooth characteristics. Moreover, the stochastic P-bifurcation and D-bifurcation can occur when the constraint position changes. |
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| Keywords: | shape memory alloy stochastic averaging probability density function stochastic P-bifurcation stochastic D-bifurcation |
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