In this paper, the singularity theory is utilized to investigate 1 ∶1 resonant bifurcations of the symmetric cross?ply composite laminated plates with two detuning parameters and an in?plane excitations. Based on the averaged equation, the restricted tangent space is obtained for the bifurcation equations with two detuning parameters and an in?plane excitations. The singularity theory is developed for the general nonlinear dynamic equation with the two state variables and four parameters. The universal unfoldings of bifurcation equation with codimension 4 are then obtained in the case of 1 ∶1 internal resonance. The transition sets in the parameter plane and the bifurcation diagrams are depicted. The relationships among two detuning parameters and an in?plane excitations are determined when the bifurcation, hysteresis and double limit point occurr. The numerical results also indicate that the number of solutions in different bifurcated regions is different.
郭宇红,张伟,杨晓东.1 ∶1内共振情况下轻质材料层合板动力学的奇异性分析[J].动力学与控制学报,2018,16(1):6~20; Guo Yuhong, Zhang Wei, Yang Xiaodong. Singularity analysis on dynamics of light⁃weight sandwichplate under 1∶1 resonance[J]. Journal of Dynamics and Control,2018,16(1):6-20.
