负泊松比蜂窝夹层板的多周期运动研究

MULTIPLE PERIODIC MOTIONS OF A HONEYCOMB SANDWICH PLATE WITH NEGATIVE POISSON’S RATIO

发展高维Melnikov方法研究含参非线性动力系统的多周期解分岔问题,并应用于研究负泊松比蜂窝夹层板的多周期运动等复杂非线性动力学行为.通过建立曲线坐标与Poincaré映射,发展适用于四维含参非线性动力系统的Melnikov函数,获得系统多周期解的存在性及个数判定定理.将所得理论结果应用于研究面内激励与横向激励共同作用下负泊松比蜂窝夹层板的多周期运动,获得系统周期轨道的存在性、个数及相应的参数控制条件.探讨横向激励系数对系统动力学行为的影响,得到在一定参数条件下,系统最多存在4个周期轨道,并利用数值模拟方法给出其相图构型,验证理论结果的正确性.

A high-dimensional Melnikov method is developed to study bifurcations of multiple periodic solutions of nonlinear dynamical systems with parameters,and applied to study of complex nonlinear dynamical behaviors such as multiple periodic motions of honeycomb sandwich plates with negative Poisson’s ratio. By constructing the curvilinear coordinates and Poincaré map,the Melnikov function suitable for a four-dimensional nonlinear dynamical system with parameters is developed. The decision theorems on existence and number of multiple periodic solutions are obtained. Based on the theoretical results,the multiple periodic motions of honeycomb sandwich plate with negative Poisson’s ratio under inplane and transverse excitations are investigated. The existence,number and parameter control conditions of periodic orbits are derived. The influence of transverse excitation on the system’s dynamical behaviors is discussed. Under certain parameter conditions,there exist at most four periodic orbits,and the phase portrait configurations are given by numerical simulations to verify the theoretical results.