Analysis Of SMA Dynamical Behavior Based On Constrained Bifurcation Theory

In the paper, the application of superelasticiity of SMA in two vibration control field is analyzed. The main work is divided into the following three aspects:Part I The properties and the researchful state of SMA are briefly introduced, the application of SMA in engineering field is reviewed.Part II With average method, taking the double-flag style hysteretic character of SMA into account, the amplitude to frequency response is derived. Aiming at the character of piecewise of the system, based on constrained bifurcation theory, the construction of transition varieties is built, calculated 12 kinds of bifurcation diagram, found that the system have soft character caused by the flag hysteretic. The numeric result shows that SMA gives rise to complicate dynamics, such as, the occurrence of multivalued steady-state solutions, jump, period 3 response, etc. From the comparison of linear and SMA system, found that near the nature frequency, SMA spring can deduct the amplitude of vibration to a certain degree, especially when the excite amplitude is high, the result is more efficient.Part III Based on the nonlinear theory of the symmetric orthotropic elastic laminates and the double-flag SMA model, the frequency-response equation under external force excitation is established for the SMA reinforced composite beam by using Galerkin approximate method and average method. Aiming at the character of piecewise of the system, based on constrained bifurcation theory, the construction of transition varieties is built,the effects of strain of forced response behavior during phase transformation from Martensite to Austenite are significant.