基于时域配点法的充液储箱系统多模态方程求解  

Solving the Multi-Dimensional Modal Equations of Liquid-Filled Container System Using the Point Collocation Method

作　　者：齐圆华[1] 齐凯华 钟裕林[1] QI Yuan-hua QI Kai-hua ZHONG Yu-lin(Basic Department Hainan College of Software Technology, Qionghai 571400, China Shanghai Engineering Center for Microsatellites, Shanghai 200120, China)

机构地区：[1]海南软件职业技术学院基础部,海南琼海571400 [2]上海微小卫星工程中心,上海200120

出　　处：《数学的实践与认识》2017年第5期90-97,共8页Mathematics in Practice and Theory

摘　　要：采用时域配点法研究了充液储箱系统多模态方程的稳态周期解.在模型求解过程中,利用牛顿迭代法求解了配点法得到的非线性代数方程组,而牛顿迭代的初值来自谐波平衡法求解得到的低阶谐波近似.数值仿真结果验证了时域配点法的有效性,并验证以二倍激励频率为基频的第二模态的假设形式更为有效.最终通过对比谐波系数数量级提出一种更为简洁有效的模态表达形式.In this study, the multi-dimensional modal nonlinear equations of liquid-filled container system was investigated by using the time domain point collocation method. To solving nonlinear algebraic equations, Newton iterative method was used and initial values were got by solved the corresponding low order harmonic approximation with Harmonic balance method. Numerical simulation results show the time domain collocation method are effective and the second mode in the form with the twice excitation frequency as fundamental frequency was proved to be more efficient. In addition, we present a more concise and effective expression by comparing the magnitude of modal harmonic coefficients.

关 键 词：充液储箱系统 时域配点法 谐波分量 

分 类 号：O241.6[理学—计算数学]