Probability Response of Shape Memory Alloy Beam Subjected to Noise Excitation

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.