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力学书籍/力学/Dynamics of Multibody Systems (Shabana A.A.) (Z-Library)/auto/Dynamics of Multibody Systems (Shabana A.A.) (Z-Library).md

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 Lumped Masses In this section, the kinetic energy of the deformable body was developed in terms of a finite set of coordinates. This was achieved by assuming the deformation shape using the body shape functions that depend on the spatial coordinates. Therefore, the deformation at any point on the body can be obtained by specifying the coordinates of this point in the body shape function. This approach leads to what is called consistent mass formulation. Another approach that is also used to formulate the dynamic equations of deformable bodies is based on using lumped mass techniques. In the lumped mass formulation the interest is focused on the displacement of selected grid points on the deformable body. Instead of using shape functions, a set of shape vectors are used to describe the relative motion between these grid points. These shape vectors can be assumed or can be determined experimentally. They can also be the mode shapes of vibration of the deformable body. In the lumped mass formulation the total mass of the body is distributed among the grid points. By increasing the number of the grid points more accurate results can be obtained.  
-**块状质量**
+**集总质量**
 
 在本节中，我们根据有限坐标集推导了变形体的动能。这通过假设依赖于空间坐标的形函数来描述变形形状来实现。因此，通过在形函数中指定该点的坐标，可以获得体上任意一点的变形。这种方法导出了所谓的“一致质量公式”。另一种用于建立变形体动力学方程的方法是基于块状质量技术。在块状质量公式中，重点关注变形体上选定网格点的位移。代替使用形函数，使用一组形向量来描述这些网格点之间的相对运动。这些形向量可以是假设的，也可以是实验确定的。它们也可以是变形体的振动模式。在块状质量公式中，变形体的总质量被分配到网格点上。通过增加网格点的数量，可以获得更准确的结果。
 
 In the remainder of this section we develop the inertia properties of deformable bodies that undergo finite rotations using a lumped mass technique. This development leads to a set of inertia shape matrices similar to the ones that appeared in the consistent mass formulation. As pointed out earlier, in the lumped mass formulation, the motion of the deformable body is identified by a set of shape vectors that describe the displacement of selected grid points. The shape vectors should be linearly independent and should contain the low-frequency modes of vibration of the body. In this section, grid point displacements are expressed in terms of the elastic generalized coordinates of the deformable body. The deformation vector of a grid point $j$ on body $i$ can be written as  
+在本文的后续部分，我们将使用集总质量技术，发展经历有限转动的变形体的惯性性质。这一发展将导出一个惯性形状矩阵集合，类似于一致质量公式中出现过的矩阵。正如前面指出的，在集总质量公式中，变形体的运动由一组形状向量来描述，这些向量描述了选定网格点的位移。这些形状向量应线性无关，并且应包含该体的低频振动模式。在本节中，网格点位移将以变形体的弹性广义坐标来表达。体 $i$ 上网格点 $j$ 的变形向量可以写为：
+
 
 $$
 \bar{\mathbf{u}}_{f}^{i j}=\mathbf{N}^{i j}\mathbf{q}_{f}^{i},\quad j=1,2,\ldots,n_{j}
 $$  
 
 where $\bar{\mathbf{u}}_{f}^{i j}$ is the vector of elastic deformation at the grid point $j_{:}$ ${\bf q}_{f}^{i}$ is the vector of elastic coordinates of body i, $\mathbf{N}^{i j}$ is a partition of the assumed shape matrix associated with the displacements of the grid point $j$ , and $n_{j}$ is the total number of the grid points. The partition $\mathbf{N}^{i j}$ is $3\times n_{f}$ matrix, where $n_{f}$ is the total number of elastic coordinates of body $i.$ . As pointed out earlier, the body shape matrix can be determined experimentally by using modal testing or numerically by first using the finiteelement method to discretize the deformable body and then solve for the eigenvalue problem.  
+其中，$\bar{\mathbf{u}}_{f}^{i j}$ 是网格点 $j$ 处的弹性变形矢量；${\bf q}_{f}^{i}$ 是实体 i 的弹性坐标矢量；$\mathbf{N}^{i j}$ 是与网格点 $j$ 的位移相关的假定形状矩阵的划分；$n_{j}$ 是网格点的总数。该划分 $\mathbf{N}^{i j}$ 是一个 $3\times n_{f}$ 矩阵，其中 $n_{f}$ 是实体 i 的弹性坐标总数。正如前面指出的，可以通过模态试验或首先使用有限元方法离散化可变形实体并求解特征值问题，来实验性地确定实体形状矩阵。
 
 The global position of the grid point $j$ can be written as