Stochastic Bifurcation and First-passage Failure of the Shape Memory Alloy Beam Subjected to Stochastic Excitation

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Journal of Vibration and Shock ›› 2012, Vol. 31 ›› Issue (9) : 24-28.

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Stochastic Bifurcation and First-passage Failure of the Shape Memory Alloy Beam Subjected to Stochastic Excitation

Wang Hong-li, Yao Shi-lei, Ge Gen, Xu Jia

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Abstract

Based on the isostrain loading and unloading experimental data of SMA (Shape Memory Alloy), the van der Pol cycle model was used to characterize the hysteretic nonlinearity of this material. According to the theory of elastic and Galerkin’s method, the vibration model is built for the beam excited by the Gaussian noise. The Hamilton function has been described as one dimension diffusion process by using stochastic average method for quasi-non-integrable- Hamiltonian systems. Using the largest Lyapunov exponent and the singular boundary theory simultaneously, both the local and global stability of the system are studied. The stochastic Hopf bifurcation is analyzed by the changes of stationary and joint probability densities. Finally, the Backward Kolmogorov equation for the reliability function and the first-passage time has been established, the numerical results are given with the boundary and initial conditions.

Key words

SMA beam / Stochastic Stability / Hopf bifurcation / Reliability Function / First-passage Failure

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Wang Hong-li;Yao Shi-lei;Ge Gen;Xu Jia. Stochastic Bifurcation and First-passage Failure of the Shape Memory Alloy Beam Subjected to Stochastic Excitation[J]. Journal of Vibration and Shock, 2012, 31(9): 24-28