【摘要】 主要利用推广的四维次谐Melnikov方法研究一类面内载荷与横向载荷联合作用下四边简支矩形蜂窝夹芯板的周期运动.首先,通过引入周期变换和相应的Poincaré映射,获得一个四维次谐Melnikov向量函数,通过对该向量函数简单零点的研究,得到一类四维非线性非自治系统周期运动的存在性判定定理.然后,利用推广的四维次谐Melnikov方法研究了1∶2内共振情况下蜂窝夹芯板的周期运动,获得了系统存在两倍周期运动的参数域.最后,对系统进行数值模拟,验证了理论分析的正确性.更多还原

【Abstract】 The periodic motion of a simply-supported rectangular honeycomb sandwich plate under the combination of the parametric and transverse excitations is investigated by the improved four-dimensional subharmonic Melnikov method. Based on periodic transformations and Poincaré map,a four-dimensional subharmonic Melnikov function is obtained. Then,a main theorem,which can be used to determine the existence of the periodic orbits for the four-dimensional non-autonomous nonlinear dynamical system,is presented. The periodic motion of the honeycomb sandwich plate under 1∶ 2 internal resonance is then studied by the improved method. The certain parameter regions where the period-two motion may occur are obtained. Numerical simulations are also carried out to verify the analytical predictions.更多还原