基于林滋泰德-庞加莱法的达芬系统的求解  

Solution of Duffin System Based on Linz Ted-Poincare Method

作　　者：莘智[1] 侯瑾蓉 XIN Zhi;HOU Jin-rong(College of Mathematics Science,Inner Mongolia Normal University,Hohhot 010022,China)

机构地区：[1]内蒙古师范大学数学科学学院,内蒙古呼和浩特010022

出　　处：《内蒙古师范大学学报（自然科学版）》2022年第5期545-550,共6页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(11761055);内蒙古自治区自然科学基金资助项目(2017MS0123);内蒙古师范大学科研基金资助项目(2016YJRC014)。

摘　　要：利用林滋泰德-庞加莱法求解达芬系统中两种振动的解析解并提高其精度。首先,利用林滋泰德-庞加莱法将达芬系统自由振动的解析解由二阶提高到三阶,其次,将带微弱阻尼的达芬系统接近共振的受迫振动以及亚谐波共振的解析解由一阶提高到二阶。The Linz Ted-Poincaré method is applied to solve the analytical solutions of two kinds of oscillation in the Duffin system and to improve the accuracy of the solutions. In the paper,the analytical solution of the free oscillation in Duffin system is improved from the second order to the third order by using the Linz Ted-Poincaré method,and also the forced vibration near resonance and the analytical solution of subharmonic resonance of Duffin system with weak damping are improved from the first order to second order.

关 键 词：林滋泰德-庞加莱法 达芬系统 弱非线性系统 

分 类 号：O322[理学—一般力学与力学基础]