How many points are enough when running a modal test?

Let's discuss this

进行模态试验时，多少点才够用？

那我们讨论一下这个问题吧

 

I expected that eventually you would get around to asking me that question. It’s another one that I get asked all the time. Basically the simplest answer is that you need to measure a sufficient number of points so that you can uniquely describe the mode shape. This answer may not be completely obvious. We need to talk about this a little more.

我料想你最终会来问我那个问题。它是另一个我经常会被问到的问题。大致说来最简单的回答是，你需要测量足够多的点，这样你就可以唯一地描述模态振型了。这个回答可能不是十分显而易见。我们需要再多讨论一下这个问题。

 

Let's start with a simple structure that we have discussed before. The simple plate structure is shown below.

我们从先前讨论过的简单结构开始。这个简单的平板结构如下所示。

Now from the mode shapes shown we can see that there are sufficient number of points to describe the mode shape for each mode. But there are a total of 45 measurement locations on this plate.

从图示的模态振型中，我们现在可以看出，有足够数量的点来描述每一阶模态的振型。可是在这个平板上共有45个测点位置。

 

Now let's consider only 5 points along one edge of the plate to illustrate some important points. If I look at mode 1 and mode 3, I quickly realize that there are not enough points to adequately describe the differences between the two modes. And also considering mode 2 and mode 4, the same conclusion can be drawn.

现在，为了阐明一些重点内容，让我们仅考虑沿着平板一条边上的5个测点。如果我观察1阶和3阶模态，我很快意识到，这里没有足够多的点来充分描述这两阶模态之间的差别。另外，考虑2阶和4阶模态，也可以得到相同的结论。

But I think we would all realize that only 5 points will not be sufficient to adequately describe the mode shape. Would it be possible to measure the mode reasonably well with only 15 measurement points? Well, most likely - but it is heavily dependent on where the 15 points are located. Let's consider 15 points - but I am going to pick the points to illustrate a point.

但是我认为我们应该都能够意识到，要充分描述模态振型，仅有5个测点是不够的。只用15个测点，有可能将模态测量得相当不错吗？嗯，有可能吧 — 但它很大程度上依赖于这15个测点布置在什么位置。让我们考虑15个测点 — 但是我将选取一些点来阐明一个重点内容。

If I look at these 15 points then it is very hard to distinguish between mode 1 and mode 3. For all practical purposes, the mode shapes look almost exactly the same.

如果我观察这15个测点，那么1阶模态和3模态之间很难区分。实际上，这些模态振型看上去几乎完全相同。

 

Now let's consider that we only took measurements along the front and back edges of the plate. You would be very hard pressed to tell the difference between the first rigid body mode and the first flexural mode.

现在我们考虑，仅仅沿着平板的前、后边缘进行测量。你会很难区分第1阶刚体模态和第1阶弹性体模态之间的差别。

So from all of these simple examples above, it becomes obvious that we need a distribution of points located appropriately such that each mode shape can be uniquely distinguished. If I am only interested in characterizing mode 1 and mode 2, then possibly I could get a fairly good description with only 6 points as shown but fewer points than that would be difficult especially if we needed to distinguish the flexible modes from the rigid body modes.

因此根据上面的所有这些简单例子，很明显，我们需要测点恰当地分布，以便唯一地区分每一阶模态振型。如果我只对1阶模态和2阶的特性感兴趣，则只用图示的6个测点，就有可能得到相当好的振型描述。但是，比那更少的测点就难了，特别是如果我们需要将刚体模态和弹性体模态区别开来。

Now let's consider another example - the simple frame shown. Suppose that the only surfaces that are accessible are the three exterior surfaces. If I only collected measurements on those surfaces and did not have any measurements on the interior surface, then the description of the mode shapes may not be sufficient to uniquely describe the mode shapes. Just consider mode 2 and mode 4. In one mode, the two cross beams are out of phase with each other and for the other mode they are in phase with each other. The same is true for mode 5 and mode 6. If there are no measurements available on the interior surface then it is very difficult to distinguish the mode shapes for these modes. This is a common testing problem that occurs in many modal tests. Too few points are used to describe the mode shape due to inaccessibility of all the significant modally active portions of the structure.

现在我们来考虑另外一个例子 — 图中所示的简单框架。假设可以获取的平面仅为三个外平面。如果仅仅采集这些平面上的测量结果，并且没有内部平面上的任何测量结果，那么这些模态振型的描述可能不足以唯一地确定模态振型。仅仅考虑2阶和4阶模态，某一阶模态当中，两个横梁相互之间是反相的，而对于另外一阶模态，它们相互之间又是同相的。对于5阶和6阶模态，情况也同样如此。如果没有得到内部平面上的测量结果，那么将很难区分这些模态的振型。这是在很多模态试验中发生的常见试验问题。由于无法得到结构的全部重要的模态活动部分，造成可用的测点太少，以至于不能确定模态振型。

 

Another common problem encountered in performing a modal test is the reluctance to measure adjacent portions of a structure. A typical comment that will be made is that we are only interested in a portion of a structure that we have responsibility for. We are not interested in the rest of the structure because it doesn't fall under our jurisdiction. To illustrate the problem with this statement we can also use the simple frame again.

进行模态试验时，另一个常见的问题是不愿意去测量结构的相邻部分。会做的典型解释是我们只对我们负责的结构部分感兴趣。我们对结构的其他部分不感兴趣，因为它不在我们的管辖范围之内。为了说明这种说法的问题，我们可以再次利用这个简单框架。

But this time measurements and modal data are only collected for the interior surface of the structure.  We can quickly see that some of the mode shape information is strongly controlled by the exterior of the structure. If we don't measure enough information to fully describe the mode shape, then it may be very difficult to determine what the cause of the problem is when we blindly limit the data we look at.

但这次只采集结构内部平面的测量结果和模态数据。我们很快可以发现，某些模态振型信息是由结构外部极大地支配的。如果没有测量足够多的信息来充分地描述模态振型，当盲目地局限于所观察的数据的时候，或许很难确定问题的原因是什么。

A good example of this brings to mind a recent modal test on a troublesome torsional vibration shaker system. The folks interested in solving their problem were only interested in the fixture and test article that came under their responsibility. Their impression of the shaker system and supporting structure was that they really didn't care what the outside world was doing. But in fact, the rest of the structure was actually responsible for the trouble that they were experiencing. The local response on the fixture and test article was largely due to some major global modes of the system. Without measuring this information, you would not have sufficient data to correct or understand the problem.

这个很好的例子使我想起了近期的一次模态试验，试验是在一个棘手的扭转振动台系统上进行的。想要解决他们问题的试验人员只对他们职责范围内的夹具和试件感兴趣。他们对振动台系统和支撑结构的感觉是他们真的不在乎外部世界正在做什么。但是事实上，其他结构实际上是造成他们遇到的问题的原因。夹具和试件上的局部响应大部分是由某些重要的系统全局模态产生的。如果不测量这些信息，你就没有足够的数据来纠正问题或者去理解问题。

 

Now I hope you have a better understanding of how many points are needed for a modal test - a sufficient number to uniquely identify the mode. If you have any other questions about modal analysis, just ask me.

现在对于需要多少个点进行模态试验，我希望你有了更好的理解 — 数量足够多，多到可以唯一地确定模态。如果你有关于模态分析的任何其他问题，尽管问我好了。