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| Abstract: |
| Shape Memory Alloy (SMA) is a typical material with memory effect, and it is widely used in many engineering fields. Based on the elastic theory and Galerkin method, a vibration system of SMA beam with rigid constraints is proposed. The non-smooth transformation was employed to deal with the discontinuous position, and the original system was turned into an approximate equivalent system associated with the Dirac function. Then, using the stochastic averaging method, the drift and diffusion coefficients of the corresponding Fokker Planck Kolmogorov equation were described. Lastly, the approximate probability response of the system was formulated analytically. Meanwhile, numerical simulation was carried out to verify the effectiveness of analytical results. Furthermore, stochastic bifurcation was discussed. Results show that the stationary probability response of the system was affected by the increase of noise amplitude and restitution force, and a certain restitution value and damping could induce P-bifurcation. |
| Key words: Shape Memory Alloy stochastic averaging stationary probability density stochastic bifurcation |
| DOI：10.11916/j.issn.1005-9113.2019047 |
| Clc Number:O194 |
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| Descriptions in Chinese: |
| 噪声激励下形状记忆合金梁的概率响应 李玉婷，冯进钤，王迎宵 （西安工程大学 理学院，西安 710000） 摘要：形状记忆合金是一种具有记忆效应和超弹性的材料，广泛应用于各个工程领域中。 基于弹性理论和Galerkin方法，本文提出了具有刚性约束的形状记忆合金梁的振动模型。应用随机平均法，得到该模型的概率响应。同时，通过数值模拟验证解析结果的正确性，从而证明了该随机平均法的有效性。 此外，讨论了随机分岔现象。 结果表明，一定的碰撞恢复力和阻尼力会引起P分岔。 关键词：形状记忆合金；随机平均；稳态概率密度；随机分岔 |
