非线性大挠度矩形板中内共振导致的分叉

BIFURCATION ANALYSIS OF A NONLINEAR RECTANGULAR PLATE WITH LARGE DEFLECTION

研究了一个非线性大挠度矩形板在简谐激励作用下的动力学行为 .利用Galerkin原理和平均法建立了这一非线性系统的双模态模型 ,讨论了由于内共振导致的分叉行为 ,最后利用数值分析证实了理论分析得到的结论 .

The dynamic behavior of a nonlinear plate subjected to simple harmonic excitation is studied. Using the Galerkin principle, the double mode model is presented. The bifurcation behavior of the plate is examined in detail in the case of internal response. The method of averaging is used to derive a set of autonomous equations. The averaged differential equations are then examined to determine their bifurcation behavior. Finally, the results of theoretical analysis are numerically verified.