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.obsidian/plugins/copilot/data.json vendored
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@ -171,6 +171,22 @@
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4
多体+耦合求解器/参考文献/Craig-Coupling of substructures for dynamic an/auto/Craig-Coupling of substructures for dynamic an.md
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@ -566,7 +566,7 @@ $$
The zeros in these matrices are the result of orthogonality (e.g., Eqs. (37) and (38)), and the residual flexibility term $\Psi_{b b}$ of $\bar{K}_{R}^{c}$ is due to Eq. (35).s The above formulation is a consistent Ritz transformation; residual effects are included in both the stiffness and mass matrices. If the residual term $\bar{M}_{b b}$ in the mass matrix is omitted, the resulting nonconsistent transformation is referred to as the MacNeal method[6]. The zeros in these matrices are the result of orthogonality (e.g., Eqs. (37) and (38)), and the residual flexibility term $\Psi_{b b}$ of $\bar{K}_{R}^{c}$ is due to Eq. (35).s The above formulation is a consistent Ritz transformation; residual effects are included in both the stiffness and mass matrices. If the residual term $\bar{M}_{b b}$ in the mass matrix is omitted, the resulting nonconsistent transformation is referred to as the MacNeal method[6].
As suggested by Martinez, et al., let the lower partition of Eq. (65) be solved for the generalized coordinate vector $\pmb{p_{b}}$ in terms of $\mathbf{\deltau}_{b}$ , and the result incorporated back into the upper partition of Eq. (65). Finally, Eq. (65) can be re-cast in terms of the modal generalized coordinate vector $\pmb{p}_{k}$ and the interface displacement vector $\pmb{u}_{b}$ . This produces the following coordinate-transformation equation: As suggested by Martinez, et al., let the lower partition of Eq. (65) be solved for the generalized coordinate vector $\pmb{p_{b}}$ in terms of $\mathbf{\deltau}_{b}$ , and the result incorporated back into the upper partition of Eq. (65). Finally, Eq. (65) can be re-cast in terms of the modal generalized coordinate vector $\pmb{p}_{k}$ and the interface displacement vector $\pmb{u}_{b}$ . This produces the following coordinate-transformation equation:
正如 Martinez 等人所建议的那样，将方程 (65) 的下部分块求解为广义坐标向量 $\pmb{p_{b}}$ 关于 $\mathbf{\deltau}_{b}$ 的表达式，并将结果重新代入方程 (65) 的上部分块。最终，方程 (65) 可以用模态广义坐标向量 $\pmb{p}_{k}$ 和接口位移向量 $\pmb{u}_{b}$ 重写。由此得到以下坐标变换方程：
$$ $$
\begin{array}{r l r}{\lefteqn{\boldsymbol{u}^{c}\equiv\left\{\begin{array}{l}{\boldsymbol{u}_{i}}\\ {\boldsymbol{u}_{b}}\end{array}\right\}^{c}}}\\ &{=}&{\left[\begin{array}{l l}{\tilde{\Phi}_{i k}}&{\tilde{\Psi}_{i b}}\\ {0_{b k}}&{I_{b b}}\end{array}\right]^{c}\left\{\begin{array}{l}{\boldsymbol{p}_{k}}\\ {\boldsymbol{u}_{b}}\end{array}\right\}^{c}}\end{array} \begin{array}{r l r}{\lefteqn{\boldsymbol{u}^{c}\equiv\left\{\begin{array}{l}{\boldsymbol{u}_{i}}\\ {\boldsymbol{u}_{b}}\end{array}\right\}^{c}}}\\ &{=}&{\left[\begin{array}{l l}{\tilde{\Phi}_{i k}}&{\tilde{\Psi}_{i b}}\\ {0_{b k}}&{I_{b b}}\end{array}\right]^{c}\left\{\begin{array}{l}{\boldsymbol{p}_{k}}\\ {\boldsymbol{u}_{b}}\end{array}\right\}^{c}}\end{array}
$$ $$
@ -590,7 +590,7 @@ Figure 12: R-M Transformation Matrix-Cols. 5--8.
# 5. Conclusions and Recommendations # 5. Conclusions and Recommendations
Procedures used to formulate component modes for substructures and to assemble substructure models to form reduced-order models of the original system have been reviewed. The physical meaning of many CMS terms has been illustrated. The constraint-mode method described in Section 4.1 is widely used in reducing finite element models for dynamic analysis because it is very straightforward, and it leads to accurate reduced-order models. On the other hand, the attachment-mode method described in Section 4.2 also produces accurate reduced-order models, and is currently widely used in test-verifying finite element models. There is a pressing need for the development of efficient computational structural dynamics algorithms based on constraint-mode substructuring methods, and there is still a substantial need for a more thorough understanding of attachment-mode methods and their use in test verification of finite element models. Research is also needed on CMS methods for damped structural systems. Procedures used to formulate component modes for substructures and to assemble substructure models to form reduced-order models of the original system have been reviewed. The physical meaning of many CMS terms has been illustrated. The constraint-mode method described in Section 4.1 is widely used in reducing finite element models for dynamic analysis because it is very straightforward, and it leads to accurate reduced-order models. On the other hand, the attachment-mode method described in Section 4.2 also produces accurate reduced-order models, and is currently widely used in test-verifying finite element models. There is a pressing need for the development of efficient computational structural dynamics algorithms based on constraint-mode substructuring methods, and there is still a substantial need for a more thorough understanding of attachment-mode methods and their use in test verification of finite element models. Research is also needed on CMS methods for damped structural systems.
已对用于制定子结构的组件模态以及将子结构模型组装成原系统的降阶模型的程序进行了回顾。许多 CMS 术语的物理意义已被阐明。第 4.1 节所述的约束模态方法在动态分析中广泛用于简化有限元模型，因为它非常直观，并能得到准确的降阶模型。另一方面，第 4.2 节所述的附着模态方法也能产生准确的降阶模型，并且目前在有限元模型的试验验证中被广泛使用。迫切需要基于约束模态子结构方法开发高效的计算结构动力学算法，并且仍然需要更深入地理解附着模态方法及其在有限元模型试验验证中的应用。还需要对阻尼结构系统的 CMS 方法进行研究。
# 6. References # 6. References
[1] Bisplinghoff, R. L., Ashley, H., and Halfman, R. L., Aeroelasticity, Addison-Wesley Publishing Co., Inc., Reading, Ma, 1955. [1] Bisplinghoff, R. L., Ashley, H., and Halfman, R. L., Aeroelasticity, Addison-Wesley Publishing Co., Inc., Reading, Ma, 1955.