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

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Journal of Vibration and Shock ›› 2021, Vol. 40 ›› Issue (17) : 1-6.

LI Yuting1, FENG Jinqian1, YUE Xiaole2

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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.

Key words

impact / shape memory alloy (SMA) / probability response / stochastic bifurcation / stochastic averaging

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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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