diff --git a/.obsidian/plugins/copilot/data.json b/.obsidian/plugins/copilot/data.json index 6a7a051..090a3ea 100644 --- a/.obsidian/plugins/copilot/data.json +++ b/.obsidian/plugins/copilot/data.json @@ -172,6 +172,20 @@ "stream": true, "displayName": "gemini-2.5-flash-balance", "enableCors": true + }, + { + "name": "ministral-3:14b", + "provider": "ollama", + "enabled": true, + "isBuiltIn": false, + "baseUrl": "https://possibly-engaged-filly.ngrok-free.app/", + "apiKey": "", + "isEmbeddingModel": false, + "capabilities": [ + "vision" + ], + "stream": true, + "enableCors": true } ], "activeEmbeddingModels": [ diff --git a/书籍/力学书籍/OpenFast/FASTKinetics/auto/Blade.md b/书籍/力学书籍/OpenFast/FASTKinetics/auto/Blade.md new file mode 100644 index 0000000..409b47c --- /dev/null +++ b/书籍/力学书籍/OpenFast/FASTKinetics/auto/Blade.md @@ -0,0 +1,155 @@ + + +The distributed properties of blade 1 bring about generalized inertia forces and generalized active forces associated with blade elasticity, blade damping, blade weight, and blade aerodynamics. + +$$ +F_{r}^{*}\big|_{Bl} = -\int_{0}^{Bl \, dFlexL} \mu^{Bl}(r) \, {}^E \, \boldsymbol{v}_{r}^{SI}(r) \cdot E \, \boldsymbol{a}^{SI}(r) \, dr - m^{BldTip} \, {}^E \, \boldsymbol{v}_{r}^{SI}(Bl \, dFlexL) \cdot {}^E \, \boldsymbol{a}^{SI}(Bl \, dFlexL) \quad (r = 1, 2, \ldots, 22) +$$ + +其中 +$$ +\mu^{B1}(r) = AdjBlMs^{B1} \cdot BMassDen^{B1}(r) +$$ + +$$ +m^{B1Tip} = TipMass(1) +$$ +or, + +$$ +F_{r}^{*}\big|_{B1} = -\int_{0}^{BldFlexL} \mu^{B1}(r) \, {}^E\boldsymbol{v}_{r}^{SI}(r) \cdot \left\{ +\begin{array}{l} +\left( \sum_{i=1}^{14} {}^{E}\boldsymbol{v}_{i}^{SI}(r) \ddot{q}_{i} \right) + \left( \sum_{i=16}^{18} {}^{E}\boldsymbol{v}_{i}^{SI}(r) \ddot{q}_{i} \right) + {}^{E}\boldsymbol{v}_{Teet}^{SI}(r) \ddot{q}_{Teet} \\ ++ \left[ \sum_{i=4}^{14} \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{i}^{SI}(r) \right) \dot{q}_{i} \right] + \left[ \sum_{i=16}^{18} \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{i}^{SI}(r) \right) \dot{q}_{i} \right] + \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{Teet}^{SI}(r) \right) \dot{q}_{Teet} +\end{array} +\right\} dr \\ +- m^{B1Tip} {}^{E}\boldsymbol{v}_{r}^{SI}(BldFlexL) \cdot \left\{ +\begin{array}{l} +\left( \sum_{i=1}^{14} {}^{E}\boldsymbol{v}_{i}^{SI}(BldFlexL) \ddot{q}_{i} \right) + \left( \sum_{i=16}^{18} {}^{E}\boldsymbol{v}_{i}^{SI}(BldFlexL) \ddot{q}_{i} \right) + {}^{E}\boldsymbol{v}_{Teet}^{SI}(BldFlexL) \ddot{q}_{Teet} \\ ++ \left[ \sum_{i=4}^{14} \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{i}^{SI}(BldFlexL) \right) \dot{q}_{i} \right] + \left[ \sum_{i=16}^{18} \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{i}^{SI}(BldFlexL) \right) \dot{q}_{i} \right] \\ ++ \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{Teet}^{SI}(BldFlexL) \right) \dot{q}_{Teet} +\end{array} +\right\} \quad (r = 1, 2, \ldots, 14; 16, 17, 18; Teet) +$$ + +因此， + +$$ +\left[C(q,t)\right]_{B1} (\text{Row,Col}) = \int_{0}^{BldFlexL} \mu^{B1}(r) \, {}^{E}\boldsymbol{v}_{\text{Row}}^{S1}(r) \cdot {}^{E}\boldsymbol{v}_{\text{Col}}^{SI}(r) \, dr + m^{B1Tip} {}^{E}\boldsymbol{v}_{\text{Row}}^{SI}(BldFlexL) \cdot {}^{E}\boldsymbol{v}_{\text{Col}}^{SI}(BldFlexL) \quad (\text{Row, Col} = 1,2,\ldots,14;16,17,18;22) +$$ + +$$ +\left\{-f(\dot{q},q,t)\right\}_{B1} (\text{Row}) = -\int_{0}^{BldFlexL} \mu^{B1}(r) \, {}^{E}\boldsymbol{v}_{\text{Row}}^{SI}(r) \cdot \left\{ \left[ \sum_{i=4}^{14} \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{i}^{SI}(r) \right) \dot{q}_{i} \right] + \left[ \sum_{i=16}^{18} \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{i}^{SI}(r) \right) \dot{q}_{i} \right] + \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{Teet}^{SI}(r) \right) \dot{q}_{Teet} \right\} dr \\ +- m^{B1Tip} {}^{E}\boldsymbol{v}_{\text{Row}}^{SI}(BldFlexL) \cdot \left\{ \left[ \sum_{i=4}^{14} \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{i}^{SI}(BldFlexL) \right) \dot{q}_{i} \right] + \left[ \sum_{i=16}^{18} \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{i}^{SI}(BldFlexL) \right) \dot{q}_{i} \right] + \frac{d}{dt} \left( {}^{E}\boldsymbol{v}_{Teet}^{SI}(BldFlexL) \right) \dot{q}_{Teet} \right\} \quad (\text{Row} = 1,2,\ldots,14;16,17,18;22) +$$ + + +$$ +F_{r}\big|_{ElasticB1} = -\frac{\partial V'^{B1}}{\partial q_r} \quad (r = 1, 2, \ldots, 22) +$$ +$$ +\left. F_{r} \right|_{ElasticB1} = +\begin{cases} +- {k'}_{11}^{B1F} q_{B1F1} - {k'}_{12}^{B1F} q_{B1F2} + & \text{for } r = B1F1 \\ +- {k'}_{11}^{B1E} q_{B1E1} + & \text{for } r = B1E1 \\ +- {k'}_{21}^{B1F} q_{B1F1} - {k'}_{22}^{B1F} q_{B1F2} + & \text{for } r = B1F2 \\ +0 + & \text{otherwise} +\end{cases} +$$ + +where $k_{\ i j}^{\,\prime B I F}$ and $\boldsymbol{k\,}_{I I}^{\prime B I E}$ are the generalized stiffnesses of blade 1 in the local flap and local edge directions respectively when centrifugal-stiffening effects are not included as follows: + +$$ +{k'}_{ij}^{B1F} = \sqrt{FlStTunr^{B1}(i) \, FlStTunr^{B1}(j)} \int_{0}^{BldFlexL} EI^{B1F}(r) \frac{d^2 \phi_i^{B1F}(r)}{dr^2} \frac{d^2 \phi_j^{B1F}(r)}{dr^2} dr \quad (i, j = 1, 2) +$$ + +其中， + +$$ +EI^{B1F}(r) = AdjFlSt^{B1} \cdot FlpStff^{B1}(r) +$$ + + +$$ +{k'}_{11}^{B1E} = \int_{0}^{BldFlexL} EI^{B1E}(r) \left[ \frac{d^2 \phi_{1}^{B1E}(r)}{dr^2} \right]^2 dr +$$ + +其中， + +$$ +EI^{B1E}(r) = AdjEdSt^{B1} \cdot EdgStff^{B1}(r) +$$ + +Similarly, when using the Rayleigh damping technique where the damping is assumed proportional to the stiffness, then + +$$ +\left. F_r \right|_{DampB1} = +\begin{cases} +-\frac{\zeta_1^{B1F} {k'}_{11}^{B1F}}{\pi f^{\prime,B 1 F}_1} \dot{q}_{B1F1} - \frac{\zeta_2^{B1F} {k'}_{12}^{B1F}}{\pi f^{\prime,B 1 F}_2} \dot{q}_{B1F2} & \text{for } r = B1F1 \\ +-\frac{\zeta_1^{B1E} {k'}_{11}^{B1E}}{\pi f^{\prime,B 1 E}_1} \dot{q}_{B1E1} & \text{for } r = B1E1 \\ +-\frac{\zeta_1^{B1F} {k'}_{21}^{B1F}}{\pi f^{\prime,B 1 F}_1} \dot{q}_{B1F1} - \frac{\zeta_2^{B1F} {k'}_{22}^{B1F}}{\pi f^{\prime,B 1 F}_2} \dot{q}_{B1F2} & \text{for } r = B1F2 \\ +0 & \text{otherwise} +\end{cases} +$$ +where $\zeta_{i}^{B I F}$ and $\zeta_{i}^{B I E}$ represent the structural damping ratio of blade 1 for the $i^{\mathrm{th}}$ mode in the local flap and edge directions, $B l d F l D m p^{B 1}(i)/100$ and $B l d E d D m p^{B 1}\left(i\right)/100$ respectively. Also, ${f^{\prime}}_{i}^{B I F}$ and $\boldsymbol{f}_{\ i}^{\prime B I E}$ represent the natural frequency of blade 1 for the $i^{\mathrm{th}}$ mode in the local flap and edge directions respectively without centrifugal-stiffening effects. That is, + +$$ +f_i^{\prime B1F} = \frac{1}{2\pi} \sqrt{\frac{k_{ii}^{\prime B1F}}{m_{ii}^{\prime B1F}}} +$$ + +$$ +f_i^{\prime B1E} = \frac{1}{2\pi} \sqrt{\frac{k_{ii}^{\prime B1E}}{m_{ii}^{\prime B1E}}} +$$ + +where $m_{\ i i}^{\prime B I F}$ and $m_{\ i i}^{\prime B I E}$ represent the generalized mass of blade 1 for the $i^{\mathrm{th}}$ mode in the local flap and edge directions respectively without centrifugal-stiffening and tip mass effects as follows: + +$$ +m_{ij}^{\prime B1F} = \int_{0}^{BldFlexL} \mu^{B1}(r) \phi_i^{B1F}(r) \phi_j^{B1F}(r) \, dr \quad (i, j = 1, 2) +$$ +$$ +m_{11}^{\prime B1E} = \int_{0}^{BldFlexL} \mu^{B1}(r) \left[ \phi_1^{B1E}(r) \right]^2 dr +$$ + +Thus +$$ +[C(q,t)]_{ElasticB1} = 0 \quad \text{and} \quad [C(q,t)]_{DampB1} = 0 +$$ + +$$ +\left. \left\{ -f(\dot{q},q,t) \right\} \right|_{ElasticB1} = +\begin{pmatrix} +\vdots \\ +\vdots \\ +\vdots \\ +-k_{11}^{\prime B1F} q_{B1F1} - k_{12}^{\prime B1F} q_{B1F2} \\ +-k_{11}^{\prime B1E} q_{B1E1} \\ +-k_{21}^{\prime B1F} q_{B1F1} - k_{22}^{\prime B1F} q_{B1F2} \\ +\vdots \\ +\vdots \\ +\vdots +\end{pmatrix} +$$ + +$$ +\left. \left\{ -f(\dot{q},q,t) \right\} \right|_{DampB1} = +\begin{pmatrix} +\vdots \\ +\vdots \\ +\vdots \\ +-\frac{\zeta_1^{B1F} k_{11}^{\prime B1F}}{\pi f_1^{\prime B1F}} \dot{q}_{B1F1} - \frac{\zeta_2^{B1F} k_{12}^{\prime B1F}}{\pi f_2^{\prime B1F}} \dot{q}_{B1F2} \\ +-\frac{\zeta_1^{B1E} k_{11}^{\prime B1E}}{\pi f_1^{\prime B1E}} \dot{q}_{B1E1} \\ +-\frac{\zeta_1^{B1F} k_{21}^{\prime B1F}}{\pi f_1^{\prime B1F}} \dot{q}_{B1F1} - \frac{\zeta_2^{B1F} k_{22}^{\prime B1F}}{\pi f_2^{\prime B1F}} \dot{q}_{B1F2} \\ +\vdots \\ +\vdots \\ +\vdots +\end{pmatrix} +$$$$ +F_{r}\big|_{GravB1} = -\int_{0}^{BldFlexL} \mu^{B1}(r) \, \boldsymbol{g}^{E}\boldsymbol{v}_{r}^{SI}(r) \cdot \boldsymbol{{z}}_2 \, dr - m^{B1Tip} \boldsymbol{g}^{E}\boldsymbol{v}_{r}^{S1}(BldFlexL) \cdot \boldsymbol{{z}}_2 \quad (r = 3,4,\ldots,14;16,17,18;Teet) +$$ + +where $F_{A e r o B 1}^{S 1}(r)$ and $M_{A e r o B 1}^{M 1}\left(r\right)$ are aerodynamic forces and pitching moments applied to point S1 on blade 1 respectively expressed per unit span. Note that $M_{A e r o B 1}^{M 1}\left(r\right)$ can include effects of both direct aerodynamic pitching moments (i.e., $\mathrm{Cm})$ ) and aerodynamic pitching moments caused by an aerodynamic offset (i.e., moments due to aerodynamic lift and drag forces acting at a distance away from the center of mass of the blade element along the aerodynamic chord). +