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中文摘要：
关注动力学系统的局部几何性质,采用多辛分析方法研究了偏心冲击荷载作用下薄圆板振动特性.在探索偏心冲击荷载作用下薄圆板振动问题动力学控制方程的对称性和守恒律的对应关系基础上,对动力学控制方程在多辛体系下重新描述,并采用显式中点差分离散方法构造其多辛格式,通过对存在不同相对偏心距冲击荷载作用下的薄圆板振动过程的数值模拟,研究了相对偏心距对薄圆板振动特性的影响,同时,数值模拟结果也充分体现了多辛算法的良好保结构性能.该研究结果不仅为由于荷载作用位置误差带来的动力学响应偏差估计提供了依据,而且为偏心冲击动力学问题的研究提供了新的途径.
英文摘要：
Focused on the local geometric properties of the dynamic system,the multi-symplectic method was used to analyze the vibration behavior of the circular thin plate under eccentric impact load. Firstly,the governing equation for the vibration problem of the plate was redescribed in the multi-symplectic framework. And then,the multi-symplectic scheme was constructed with the explicit midpoint method to simulate the dynamic process of the thin plate under impact load with different relative eccentric distances.Finally,the numerical results were presented and discussed in detail,which demonstrated the structurepreserving properties of the multi-symplectic algorithm. Generally,the numerical results not only present a reference for the estimation of the dynamic responses resulting from the acting position error of the load on the structure,but also propose a newway for the study of the eccentrically impacted plate problems.
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