Abstract：The chaotic motion of nonlinear elastic straight bar that has constitutive relation of the -shape during lonitudinal vibration are investigated.The dynamic equation of bar during lonitudinal vibration is changed into differential dynamic system by Galerkin principle.The conditions that the system has homoclinic orbit or heteroclinic orbit are given ,and the parameter equations of homoclinic orbit are solved. Using the Melnikov function ,the critical conditions that the system enters chaotic states are given. The regularity of chaotic motive region with and are obtained by numerical analysis, and the bifurcation diagrams,Displacement-time history diagram,Phase-plane diagram and Poincaré map show that the system occur steady motion or chaotic motion.The further research show that the quadric nonlinear item in constitutive relation has great effect on the dynamic behavior.
2011, Vol. 30 
