外激与参激作用下非光滑形状记忆合金梁的概率响应

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振动与冲击 ›› 2021, Vol. 40 ›› Issue (17) : 1-6.

论文

李玉婷1，冯进钤1，岳晓乐2

作者信息 +

Probabilistic response of non-smooth SMA beams under external and parametric excitations

LI Yuting1, FENG Jinqian1, YUE Xiaole2

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文章历史 +

摘要

研究了非光滑形状记忆合金梁受外激与参激作用下的概率响应及分岔现象。利用非光滑变换得到与原系统等效的近似系统，应用随机平均法和随机微分方程理论知识，推导出相应的平均Fokker-Planck-Kolmogorov方程;通过非光滑逆变换得到近似系统的解析结果，并结合数值仿真对解析结果进行了验证;利用稳态响应的极值条件，进一步得到了系统发生随机分岔的临界条件，并验证了临界条件的正确性，使得随机分岔有了更加直观的预测结果。结果表明，阻尼系数以及碰撞恢复系数都可诱导系统发生随机分岔，并得到了系统产生分岔的参数临界值。

Abstract

Here, probability response and bifurcation phenomenon of a non-smooth shape memory alloy (SMA) beam under external and parametric excitations were studied.Firstly, the approximate system equivalent to the original system was obtained with the non-smooth transformation.Then, the corresponding average Fokker-Planck-Kolmogorov equation was derived using the stochastic averaging method and the stochastic differential equation theory.Finally, the analytical results of the approximate system were obtained using the non-smooth inverse transformation, and those were verified with numerical simulation.In addition, using the extreme value condition of steady-state response, the critical condition of the system having stochastic bifurcation was further obtained, and its correctness was verified to make the prediction of stochastic bifurcation more intuitive.The study results showed that both damping coefficient and coefficient of restitution can induce the system’s stochastic bifurcation; critical values of bifurcation parameters are obtained.

导出引用

李玉婷，冯进钤，岳晓乐. 外激与参激作用下非光滑形状记忆合金梁的概率响应[J]. 振动与冲击, 2021, 40(17): 1-6

LI Yuting, FENG Jinqian, YUE Xiaole. Probabilistic response of non-smooth SMA beams under external and parametric excitations[J]. Journal of Vibration and Shock, 2021, 40(17): 1-6

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