School of Mathematics,Physics and Software Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;
School of Mathematics,Physics and Software Engineering,Lanzhou Jiaotong University,Lanzhou 730070,China;
Department of Engineering Machanics,Southwest Jiaotong University,Chengdu 610031,China;
Vibration; Impact; 1:2 resonance; Codimension two bifurcation;