1∶1内共振情况下轻质材料层合板动力学的奇异性分析

摘要

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.%利用奇异性理论研究1∶1内共振情况下的点阵夹芯板的非线性动力学分叉,基于平均方程,计算出含有两个调谐参数和一个面内激励的限制切空间;对于含有两个状态变量和三个参数的一般非线性动力学方程的奇异性理论进行了推广;利用推广的奇异性理论得到1∶1内共振情况下分叉方程余维4的普适开折,画出了转迁集和分叉图;当分叉、滞后和双极限点产生时,两个调谐参数和面内激励之间的关系被确定,数值结果表明,在不同的分叉区域解的个数不同.