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书籍/力学书籍/CASEstab_theory_manual/auto/CASEstab_theory_manual.md

@@ -134,13 +134,18 @@ These coefficients and the generalized force are only functions of time $t$ and
 
 In case of a prescribed rotation of the rotor, the acceleration forces $F_{c,i}$ given by (1.8d) are centrifugal forces that stiffen the blades. To include this centrifugal stiffness in the calculation of frequencies or in the iteration steps of a time integration, we can compute the centrifugal stiffness matrix as the Jacobian of this vector function as  
 
+这些系数和广义力仅是时间 $t$ 和位移 ${\bf q}(t)$ 的函数。 (1.7) 的第一项描述了由加速度 $\ddot{\mathbf{q}}$ 引起的基频惯性力，其质量矩阵 $m_{i j}=m_{j i}$ 是对称的。第二项描述了来自子结构的陀螺力，其中位置矢量具有显式的时间依赖性 $\partial\mathbf{r}/\partial t\neq0$ ，例如，如果运动学公式基于以给定平均速度旋转的传动系统，并且传动系统动力学由围绕该速度的变化来描述。第三项描述了作用在以给定速度旋转的子结构上的离心力，或由于其他明确定义的加速度（如地震或移动基座）引起的力，当此结构模型与基础或浮体的另一个动力学模型模块化耦合时。第四项可以描述与第二项和第三项类似的科里奥利力和加速度力。例如，令广义坐标 $q_{k}$ 为传动系统的绝对旋转角度，则通过代换 $q_{k}\,=\,\Omega t+\delta q_{k}$ 可以将此运动学公式更改为具有给定平均转速的公式，其中 $\Omega$ 是给定平均速度，$\delta q_{k}$ 是新的广义坐标。部分项 $h_{i j k}\dot{q}_{k}=h_{i j k}\Omega$ 在 $j\neq k$ 的给定恒速轴承情况下将具有等于系数 $g_{i j}$ 的分量，而对于 $j=k$ 的整个项 $h_{i j k}\dot{q}_{j}\dot{q}_{k}=h_{i j k}\Omega^{2}$ 将具有等于加速度力 $F_{c,i}$ 的分量。
+
+在风轮给定旋转的情况下，由 (1.8d) 给出的加速度力 $F_{c,i}$ 是使叶片刚化的离心力。为了在频率计算或时间积分的迭代步骤中包含这种离心刚度，我们可以将离心刚度矩阵计算为该矢量函数的雅可比矩阵，如下所示：
 $$
 k_{c,i j}=\int_{\mathcal{V}}\rho\left(\frac{\partial^{2}\pmb{r}^{T}}{\partial q_{i}\partial q_{j}}\frac{\partial^{2}\pmb{r}}{\partial t^{2}}+\frac{\partial\pmb{r}^{T}}{\partial q_{i}}\frac{\partial^{3}\pmb{r}}{\partial t^{2}\partial q_{j}}\right)d\mathcal{V}
 $$  
 
 which is not a symmetric matrix due to the second term.  
 
-The fifth term of (1.7) describes the conservative forces such as gravity and elastic forces which can be defined by the potential energy $V$ . The force function given by the derivative of the scalar potential energy function depends on the kinematic formulation and the applied theory for elasticity. The sixth term of (1.7) describes the purely dissipative forces from structural damping mechanisms (e.g. material and friction), which we will model using a modal damping method described in Section... . The last term of (1.7) describes generalized non­conservative forces acting on the structure which are discussed in Chapter... .  
+The fifth term of (1.7) describes the conservative forces such as gravity and elastic forces which can be defined by the potential energy $V$ . The force function given by the derivative of the scalar potential energy function depends on the kinematic formulation and the applied theory for elasticity. The sixth term of (1.7) describes the purely dissipative forces from structural damping mechanisms (e.g. material and friction), which we will model using a modal damping method described in Section... . The last term of (1.7) describes generalized non­conservative forces acting on the structure which are discussed in Chapter..由于第二项，它不是一个对称矩阵。
+
+(1.7)式的第五项描述了保守力，例如重力和弹力，这些力可以通过势能$V$来定义。由标量势能函数导数给出的力函数取决于运动学公式和所应用的弹性理论。(1.7)式的第六项描述了来自结构阻尼机制（例如材料和摩擦）的纯耗散力，我们将使用在第...节中描述的模态阻尼方法对其进行建模。(1.7)式的最后一项描述了作用在结构上的广义非保守力，这些力将在第...章中讨论。. .  
 
 # 1.1.1 Generic topology of structure