正则模态

正则模态分析的结果表明，该文提出的投影方法速度具有三阶精度。当采用相容的压力更新公式时，压力也具有三阶精度，而且格式是稳定的；

A normal mode analysis shows that the velocity and the pressure are both third-order accurate .

模型中将炮管处理为运动支撑上的悬臂梁，取其前N阶正则模态计算炮管各断面中心的变形和转角。

Elastic deformation of the barrel is calculated by means of the preceding N orthonormal modals of the cantilever beam .

通过建立碰撞振动系统的物理模型和数学模型，利用正则模态矩阵法对碰撞振动系统进行解耦，并用解析法求解了碰撞振动系统周期运动的解析解和线性化矩阵和各个系统的Poincare映射。

By establishing physical model and mathematical model of the vibro-impact system , using regular modal matrix method to decouple the vibro-impact system , and working out the analytical solution , linear matrix and poincare mapping of different system by analytic method . 2 .

建模中采用模态综合理论的方法，由航天器结构的弹性正则模态和静变形模态组成的模态集表示结构变形，以便更有效的将结构变形的影响引入到航天器的动力学模型中。

Introducing the technology of the modal synthesis theory , the structure deformation of the spacecraft is represented with elastic normal modes and static deformation modes to consider the influence of the structure deformation on the dynamic model more effectively .

结合有限维正则弹性弯曲模态方程，提出了以地面测试的弹性模态为初值、同时估计弹性模态和气动参数的交替估计方法。

Based on the finite-dimension Canonical equations of the elastic bending mode , An alter - native estimation method for estimating elastic modes and aerodynamic parameters of elastic aircraft has been proposed when the initial value of elastic mode is known , finally , a numerical example is given ;

为了有效地求解模态一致性框架，采用了一种可分离的模态一致性正则项，多模态成对约束传递问题可以通过一种简单的交替优化的方式求解。

For efficiently solving the modalities consensus framework , we adopt a separable modalities consensus regularizer .