CHAOS AND FRACTAL BOUNDARY OF SAFE BASIN OF A SHAPE MEMORAY AOLLY BEAM SUBJECTED TO HAMONIC AND WHITE NOSIE EXCITATIONS
GeGen1 ZhuZhiWen2 ,XuJia2
1 School of Mechanical Engineering, Tianjin Polytechnic University，Tianjin 300160, China2 School of Mechanical Engineering , Tianjin University, Tianjin,300072, PR China
Abstract： The vanderpol cycle was applied to describe the hysteretic nonlinear characteristic of the strain-stress relation of a shape memory alloy （SMA）.A dynamical model of a simply supported SMA beam subject to both parametrical harmonic and external Gaussian excitation was proposed based on Galerkin’s approach. At first, the stochastic Melnikov integral was given theoretically wich means the necessary rising of noise-induced chaotic response in the system. To quantify the noise-induced chaos, the boundary of the system’s safe basin is firstly studied and it is shown to be inclusively fractal when chaos arises based on the stochastic Melnikov method. The numerical results show the efficiency of the theoretical analysis.
葛根 竺致文 许佳. 形状记忆合金梁在简谐和白噪声联合激励下的混沌及安全盆侵蚀现象[J]. , 2012, 31(23): 1-5.
GeGen ZhuZhiWen ;XuJia. CHAOS AND FRACTAL BOUNDARY OF SAFE BASIN OF A SHAPE MEMORAY AOLLY BEAM SUBJECTED TO HAMONIC AND WHITE NOSIE EXCITATIONS. , 2012, 31(23): 1-5.
2012, Vol. 31 
