That’s called the kinetic energy density, and it’s the second term of Bernoulli’s equation.

这就是所谓的动能密度， 是伯努利方程的第二项。

The first term in Bernoulli's equation takes that energy, and divides it by volume.

伯努利方程的第一项是 能量除以体积。

We see some xi's from a Bernoulli distribution.

我们从伯努利分布中看到了一些xi。

In initial studies, the tunnel model in the LECM was conceptualized as a longitudinal continuous Euler-Bernoulli beam, as its simple computation and flexibility in complex analysis.

在初步研究中，LECM 中的隧道模型被概念化纵向连续的 Euler-Bernoulli 梁，因算简单，在复杂分析中具有灵活性。

And then the variance of this Bernoulli distribution is going to be these two proportions multiplied.

然后这伯努利分布的方差就是这本比例的乘积。

The mean of this Bernoulli distribution is going to be P2.

这伯努利分布的均值将是P2。

The key is stability, and the essence is using aerodynamics, which is fundamentally based on Bernoulli's principle.

关键是稳定性， 而本质是使用空气动力学，这从根本上是基于伯努利原理的。

That's called the kinetic energy density, and it's the second term of Bernoulli's equation.

这称动能密度， 是伯努利方程的第二项。

A Euler–Bernoulli beam on a Pasternak foundation was used as a simplified model to analyze the stress of the existing tunnel.

使用 Pasternak 基础上的 Euler-Bernoulli 梁作简化模型来分析现有隧道的应力。

And then we'll come up with general formulas for the mean and variance and standard deviation of this distribution, which is actually called the Bernoulli Distribution.

然后我们将推导出这分布的平均值、方差和标准差的一般公式，这分布实际上被称贝努利分布。

And if you do that with a Bernoulli Distribution, we learned in the video on Bernoulli Distributions, that the mean of this distribution right here is going to be equal to p.

而在使用伯努利分布的情况下，我们在关于伯努利分布的视频中学到，这分布的均值就等于p。

A Euler–Bernoulli beam with a Pasternak foundation was used as a simplified model for tunnel stress analysis.

使用带有 Pasternak 基础的 Euler-Bernoulli 梁作隧道应力分析的简化模型。

The existing tunnel is equivalent to a continuous Euler–Bernoulli beam placed on a Pasternak foundation.

现有的隧道相当于放置在 Pasternak 基础上的连续 Euler-Bernoulli 梁。

To figure out really the formulas for the mean and the variance of a Bernoulli Distribution if we don't have the actual numbers.

要推导出伯努利分布的均值和方差的公式，如果我们没有实际的数值。

The reason for this phenomenon is that the Euler-Bernoulli model excludes the shearing deformation of shield tunnels compared with the Timoshenko model, leading to a smaller deformation of tunnels.

造成这种现象的原因是，与 Timoshenko 模型相比，Euler-Bernoulli 模型排除了盾构隧道的剪切变形，导致隧道变形较小。

It is because that the Euler-Bernoulli beam overestimates the internal forces within the tunnel, while the Timoshenko beam overestimates the bending stiffness of joints between rings.

这是因 Euler-Bernoulli 梁高估了隧道内的内力，而 Timoshenko 梁高估了环之间接头的弯曲刚度。

Now with this definition of this-- and this is the most general definition of a Bernoulli Distribution.

现在有了这定义——这是伯努利分布最一般的定义。

We have a Bernoulli Distribution right over here, and we know that the mean of this distribution or the expected value of this distribution is actually going to be p.

我们这里有一伯努利分布，我们知道这分布的均值或期望值实际上就是p。

Nevertheless, scholars noticed that the Euler-Bernoulli model failed to indicate the dislocation between rings, while it widely occurred in in-service shield tunnels.

尽管如此，学者们注意到 Euler-Bernoulli 模型未能指示环之间的位错，而广泛发生在服役的盾构隧道中。

To simplify the calculations, the Euler–Bernoulli beam model assumes that the tunnel section undergoing bending deformation is always perpendicular to the neutral axis, as shown in Figure 4.

了简化算，Euler-Bernoulli 梁模型假设发生弯曲变形的隧道截面始终垂直于中性轴，如图 4 所示。