Stochastic Responses and Bifurcations of Shape Memory Alloy Beam under Asymmetric Impacting Constraint
Received:April 24, 2022  Revised:May 22, 2022
Key Words: shape memory alloy   stochastic averaging   probability density function   stochastic P-bifurcation   stochastic D-bifurcation  
Fund Project:Supported by the Natural Science Foundation of Shaanxi Province (Grant No.2018JM1044).
Author NameAffiliation
Yuting LI College of Mathematics, Jilin University, Jilin 130012, P. R. China 
Jinqian FENG College of Science, Xi'an Polytechnic University, Shaanxi 710048, P. R. China 
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      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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