and another test with a y-excitation and see some different modes

Could I use an oblique angle instead ?

我用X方向激励进行试验，可以观察到一些模态

而用Y方向激励再进行一个试验，又可以观察到一些不同的模态

作为替代我能用倾斜角度吗？

 

Well, that's a very good question. It’s one that comes up often in terms of running modal tests with a shaker excitation. Of course it is totally acceptable to run one test with a shaker at some oblique angle to the structure. But the only thing we need to be careful about is to assure that we don't select the reference point at the node of a mode. Let's talk about this a little more.

嗯，问得很好。这是一个用激振器激励进行模态试验时经常会遇到的问题。当然，用激振器在与结构成一定角度的方向上进行试验是完全可以接受的。但是我们唯一需要关心的一件事情是，要确保我们选的参考点没有位于某一阶模态的节点上。让我们多讨论一点这个问题吧。

 

Let's start this discussion with a simple structure that has mode shapes that are very directional in nature. Now just what do I mean by that. That means that the response of the structure is primarily in one direction with very little or no response in the other directions for a given mode of the structure.  Yet another mode of the structure may have response in a different direction than the first mode with little or no response in the other directions.

我们用一个简单的结构来开始这个讨论，这个结构实际上具有确定方向的模态振型。那么，我说的那话是什么意思。这意味着对于某一阶特定的结构模态，响应主要在某一个方向上，并且在其他的方向上简直没有响应。而另外一阶模态可能具有与第一阶模态不同方向的响应，而在其他方向上几乎没有响应。

To illustrate this, let's consider the very simple frame shown in figure 1. We see that mode 1 of the structure has motion primarily in the horizontal direction with very little response in the vertical direction. However, mode 2 of the structure has motion primarily in the vertical direction with very little motion in the horizontal direction. We can also see that mode 3 and mode 4 follow the same trend.  Mode 5 and mode 6 have motion in both the horizontal and vertical directions with the vertical direction being slightly more predominant.

为了说明这点，考虑图1所示的这个非常简单的框架。我们看出，结构的1阶模态主要是在水平方向上运动，在垂直方向上响应一点也没有。可是，结构的2阶模态主要是在垂直方向上运动，在水平方向上没有运动。我们也可以看出，3阶和4阶模态遵循相同的趋势。5阶和6阶模态在水平和垂直方向上都有运动，垂直方向略占优势。

 

If we look at a drive point measurement in the vertical direction (as shown in figure 2) over the bandwidth of the first six modes of the structure, we notice that there are only 2 peaks that are visible in the measured frequency response function. Yet we know that there are 6 modes in this frequency range. And if we took a drive point measurement in the horizontal direction we would also notice only 4 peaks. But upon closer examination of the measurement, we would notice that the first two frequencies of each of the measurements are different.

在结构的前6阶模态的带宽范围内，如果观察垂直方向上的一个驱动点测量结果（如图2所示），那么我们注意到，在测得的频响函数中，只有2个明显的峰。但是我们知道，在这个频率范围内有6阶模态。另一方面，如果我们在水平方向上得到一个驱动点测量结果，那么也仅会观察到4个峰。但是，当更仔细地审视测量结果时，会注意到，每个测量结果的前2阶固有频率是不同的。

So now we can see that the modes cannot be seen in every measurement. That directly implies that if we were to select either one of the two measurement points shown as a reference point then clearly we would not see all the modes of the structure. But just why does that happen.

因此我们现在可以看出，在每次测量结果中有些模态是观察不到的。这直截了当地表明了如果我们选定所示的这两个测点中的任何一个作为参考点，那么很显然我们将观察不到结构的所有阶模态。但是为什么会这样。

 

Let's recall the equation for the frequency response function

让我们回忆一下频响函数方程

which (for illustration) is expanded for 3 modes

对于3阶模态，将它展开（为了示意）

This equation is described by the residues (in the numerator) and the poles (in the denominator) for each of the modes of the system in the formation of the frequency response function. We also need to remember that the residues are directly related to the mode shapes (and a scaling factor) as

对于频响函数形式中的系统每阶模态，这个方程由留数（在分子中）和极点（在分母中）来描述。我们也要记住，留数与模态振型（以及归一化因子）直接相关，如下所示

So that the frequency response function can be written either in terms of residues or mode shapes.  When written as a mode shape, then it becomes very clear that if the value of the mode shape at the reference point is zero (or almost zero) then that mode will not be seen in the frequency response function. So the trick to performing a good modal test setup is to always select a reference point where all of the modes can be seen all the time from that reference point. But sometimes this is easier said than done, especially when I am not sure what the expected modes of the system are going to be.  (It’s always easy being a Monday morning quarterback.)

所以可以根据留数或模态振型来写频响函数。当按照模态振型写时，则情况变得很清楚，如果参考点位置的模态振型值为零（或者几乎为零），那么在频响函数中将观察不到那阶模态。所以进行良好的模态试验布置的诀窍是，总要选一个参考点，任何时候从这个参考点上都可以看到所有阶模态。但是有时说到容易做到难，特别是当我不确定预期的结构模态会是什么样子的时候。（做一个放马后炮的人总是很简单。）

 

So now let's look at the first 4 modes separately. Then the optimum reference location is easily seen to be the point on the structure where the mode shape value is largest. But I quickly realize that the point is different for each of the modes. The trick is to select one point where each of the modes can be observed "reasonably well". The point where most people get hung up is in trying to think in terms of our simple rectangular coordinate system - with x, y and z directions.

所以现在我们分别看看前4阶模态。那么很容易看出最优参考点位置是结构上模态振型最大的点。但我很快意识到，对于每阶模态这个点都不同。诀窍是选一个点，可以“相当好”地观察到每一阶模态。大多数人裹足不前的地方是他们试图按照简单的直角坐标系 — 用x、y和z方向，进行思考。

 

What would happen if I tried to apply a force to the structure at a point that has a 45 degree angle to my global rectangular coordinate system? Would the reference point shown be suitable to be able to measure all the modes of interest?

如果我试图在一个点上对结构作用一个力，力与全局直角坐标系成45度角，情况又会怎样？要能测量感兴趣的所有阶模态，图示的参考点会适合吗？

The best way to answer that question is to look at the equation that forms the frequency response function. We quickly notice that the equation can be written in terms of mode shapes. When we consider the first 4 modes of the system, we notice that each mode has a component of response in this 45 degree angle. This means that this reference point would be suitable for measuring the first 4 modes of the system. However, if I take a closer look and consider modes 5 and 6, then I will quickly discover that these two higher modes will not be measured at all from this reference point. This is because, the center point on the cross member is a node point for both modes 5 and 6 of the structure.

回答这个问题的最好方法是观察构成频响函数的方程。我们很快发现可以根据模态振型来写这个方程。考虑系统的前4阶模态时，我们发现每阶模态沿着这个45度角都有响应分量。这意味着这个参考点对于测量系统的前4阶模态是合适的。但是，如果我更深入地观察，并考虑5、6阶模态，那么我很快会发现从这点参考点上根本就测量不到这两阶更高的模态。这是因为，横梁构件的中心点不但是结构5阶的节点而且也是6阶模态的节点。

 

So we could pick any point on the structure including an angle relative to the global coordinate system.  The only requirement is that the mode shape should have a significant value in relation to its mode shape; if the reference point selected is a node of a mode then I will not see that mode in the measured response. One last thing to quickly mention is that in order to obtain valid "scaled mode shapes", a drive point measurement is necessary. (We will talk about mode shape scaling in a future article.)  This means that the response must be measured at the same point and in the same direction as the applied force – this also applies to a reference measurement which is taken at an angle to the global coordinate system.

所以我们可以在结构上选取任何一个点，相对于全局坐标系存在角度。唯一的要求是，相对于那阶模态振型来说，模态振型应该具有显著的数值；如果选定的参考点是某一阶模态的节点，那么我在所测的响应中将观察不到那阶模态。最后稍稍提到的一件事情是，为了获取有效的“归一化模态振型”，需要有一个驱动点测量结果。（我们将在以后的文章中讨论模态振型归一化。）这意味着响应必须是跟作用力一样，处于同一个点，沿着同一个方向，进行测量 — 这点也适用于与全局坐标系成角度的参考点测量结果。

 

I hope this explanation helps you to understand that you can pick any angle for the reference - just as long as it’s not the node of a mode. If you have any other questions about modal analysis, just ask me.

我希望这个解释有助于你理解这点，你可以为参考点选取任意角度 — 只要它不是某一阶模态的节点即可。如果你有关于模态分析的任何其他内容，尽管问我好了。