MODAL SPACE - IN OUR OWN LITTLE WORLD

模态空间–在我们自己的小世界中   

Pete Avitabile 著  KINGSCI INSTRUMENTS-KSI科尚仪器 组织 westrongmc 译

Is there any difference between a modal test with a shaker excitation or impact excitation?

Well ... that's a good question.

The answer is yes and no.

模态试验用激振器激励还是用锤击激励有什么差别吗？

嗯… 问得好。

答案是既有差别又没有差别。

This is another question that gets asked often. There are a lot of different aspects relating to this. Let's start with some basics to understand why it is so difficult to answer this question as either yes or no.  A few simple equations are needed to help explain this.

这是另一个经常被问到的问题。关于这个问题的不同方面有很多。我们先从基础知识入手，来理解为何这个问题难以用有差别或无差别来回答。借助于几个简单公式来解释这点。

 

First, we have to remember that any system can be described by its equation of motion. Basically, the equation is simply the force balance of mass times acceleration plus damping times velocity plus stiffness times displacement which is equal to the applied force. For a number of reasons, it is easier to work with this equation in the Laplace domain. By taking the Laplace transform of the equation of motion, we can write

首先，我们需要记住任何系统都可以根据其运动方程来描述。从根本上讲，这个方程不过是力平衡方程，也即质量乘以加速度+阻尼乘以速度+刚度乘以位移=作用力。由于某些原因，这个方程在拉氏域内更容易处理。对运动方程进行拉氏变换，可写为

We use matrices to help organize all of the equations. Remember that [M], [C], [K] are the mass, damping and stiffness matrices respectively. It is very important to note that these matrices are symmetric. Therefore, the system matrix, [B(s)], is also symmetric. The system transfer function is the inverse of the system matrix given by

我们利用矩阵将所有方程组织在一起。记住[M]、 [C]、[K]分别为质量、阻尼和刚度矩阵。需要注意的是，这些矩阵是对称的。因此，系统矩阵[B(s)]也是对称的。系统传递函数为系统矩阵的逆矩阵，可写为

And, of course, you remember that the frequency response function that we measure during a modal test is nothing more than the system transfer function evaluated along the frequency axis. Most of the time, we write the frequency response function in partial fraction form, for convenience, as

而且，你自然还记得，在模态试验过程中测得的频响函数不过是沿频率轴求系统传递函数的数值。很多情况下，方便起见，我们按照部分分式的形式来书写频响函数，如下所示

and an individual term can be written as

并且单个频响可写为

So why did I bother writing out all these equations? That's because there are some very important things to note in these equations relative to your question. Remember that [B(s)] and [H(s)] are symmetric since [M], [C], and [K] are symmetric. That means that [H(jω)] is also symmetric. This implies that hij=hji which is called reciprocity. This means that you can measure the FRF by impacting point 'i' and measuring the response at point 'j' and get exactly the same FRF as impacting point 'j' and measuring the response at point 'i'. This is what is meant by reciprocity.

那么，我为何要费事地写出所有这些公式呢？这是因为在这些公式中有一些非常重要的，与你的问题相关的东西需要关注。记住[B(s)]和[H(s)]是对称的，因为[M]、[C]和[K]是对称的。这意味着[H(jω)] 也是对称的。这说明hij=hji，称为互易性。这意味着你在'i'点激励，测量'j'点响应得到的频响函数，与在'j'点激励，测量'i'点响应得到的频响函数完全相同。此即互易性所要表达的意思。

 

Now, let's consider an impact test situation for a simple beam with three measurement locations.  There are a total of nine possible input-output FRFs that could be measured. But for this case, let's put our accelerometer at point 3 and make FRF measurements by impacting the beam at point 1, 2, and 3.  We call point 3 the reference location since it is the same response point for each of the measurements that I make. Since the hammer is roving from one point to another point, the FRFs that are measured come from one row of the FRF matrix, the last row of the matrix.

现在，让我们考虑一个锤击试验的情况，针对一个有三个测点的简单梁。可能测得的输入-输出频响函数总共有9个。但对于本例，让我们在测点3位置布置加速度计，而在测点1，2，和3位置进行锤击，得到频响函数测量结果。称测点3为参考点位置，由于对于我进行的每次测量，都是以测点3为同一个响应点。由于力锤从一点到另一点逐点遍历锤击，那么测得的频响函数为频响矩阵的一行，且是矩阵的最后一行。

Before we talk about anything else, let's discuss the same set of measurements from a shaker test.  Let's place our shaker at point 3 and make FRF measurements by roving the accelerometer to point 1, 2, and 3 on the beam; note that point 3 is still the reference location since the force is applied to the same point for each measurement. Now that the force is stationary, the FRFs that are measured come from one column of the FRF matrix, the last column of the matrix.

在讨论其他问题之前，我们先讨论利用激振器试验得到的相同测量结果。将激振器布置在测点3位置，加速度计于梁上的测点1、2、和3位置逐点移动，得到频响函数测量结果。注意到，测点3仍然是参考点位置，因为对于每次测量，激振力都施加在同一个测点位置。既然激振力是不动的，那么测得的频响函数为频响矩阵的一列，且是矩阵的最后一列。

 

If I look at the measurements taken, I'll notice that h13 from the shaker test is exactly the same as h31 from the impact test. Also notice that h23 from the shaker test is exactly the same as h32 from the impact test. Well, this is what reciprocity is all about. So, from a theoretical standpoint, it doesn't matter whether I collect data from a shaker test or an impact test. The data is exactly the same - from a theoretical standpoint. In fact, there is no reason why the impact test can't be performed by impacting the same point on the structure and roving the accelerometer around to all the different measurement locations. I could draw the same analogy for the shaker test also. We could keep the response accelerometer at the same location and move the shaker from point to point (but I don't know anyone who wants to run a test that way!). The point is that from a theoretical standpoint, it doesn't matter how the data is collected as long as the input-output characteristics are obtained.

如果观察测得的频响函数，会注意到，激振器试验得到的h13与锤击试验得到的h31完全相同。同样也会注意到，激振器试验得到的h23与锤击试验得到的h32完全相同。嗯，这即是所谓的互易性。所以，从理论的角度看，不管是从激振器试验还是从锤击试验得到数据，都是无关紧要的。数据完全相同 — 从理论上看。在结构的同一点进行脉冲激励，而逐步移动加速度计到所有测点位置，锤击试验为何不能这样进行？说起来，这没有理由啊。对于激振器试验，也可以施加类似的方案。响应加速度计固定在同一个位置，而将激振器逐点移动（但是想要按照这种方式进行试验的人，我是一个也不认识！）。问题的关键是，从理论的角度看如何得到数据无关紧要，只要得到输入-输出特性即可。

 

So the answer is that there is no difference between a shaker test and an impact test. That is, from a theoretical standpoint! If I can apply pure forces to a structure without any interaction between the applied force and the structure and I can measure response with a massless transducer that has no effect on the structure - then this is true. But what if this is not the case.

因此，答案是激振器试验和锤击试验之间没有什么差别。那是从理论的角度看的！如果我可以施加一个纯粹的力于结构之上，作用力与结构之间没有任何相互影响，并且我可以用一个无质量的传感器来测量响应，它对结构没有任何影响 — 那么这个答案成立。但倘若情况并非如此，将会怎样呢？

 

Now let's think about performing the test from a practical standpoint. The point is that shakers and response transducers generally do have an effect on the structure during the modal test. The main item to remember is that the structure under test is not just the structure that you would like to obtain modal data. It is the structure plus everything involved in the acquisition of the data - the structure suspension, the mass of the mounted transducers, the potential stiffening effects of the shaker/stinger arrangement, etc. So while theory tells me that there shouldn't be any difference between the impact test results and the shaker test results, often there will be differences due to the practical aspects of collecting data.

好了，让我们从实际的角度来考虑一下试验。问题的关键是在模态试验过程中，激振器和响应传感器通常会对结构产生影响。重点是要记住，被测结构不仅仅是那个你要得到模态数据的结构。它是结构加上数据采集中所包含的一切事物 — 结构悬挂方式，所装传感器的质量，激振器/推力杆布置的潜在刚度影响。所以尽管理论讲，锤击试验结果和激振器试验结果之间不应该有任何差别，但因为采集数据的实际问题，经常会导致有差别。

 

The most obvious difference will occur from the roving of accelerometers during a shaker test. The weight of the accelerometer may be extremely small relative to the total weight of the whole structure, but its weight may be quite large relative to the effective weight of different parts of the structure. This is accentuated in multi-channel systems where many accelerometers are moved around the structure in order to acquire all the measurements. This can be a problem especially on light weight structures.  One way to correct this problem is to mount all of the accelerometers on the structure even though only a few are measured at a time. Another way is to add dummy accelerometer masses at locations not being measured; this will eliminate the roving mass effect.

最明显的差别源于激振器试验过程中的加速度计移动。相对于整个结构的总重量来讲，加速度计重量或许极其微小，但相对于结构的不同部件的有效重量来讲，其重量或许非常大。在多通道系统中，这个问题尤为突出，其中为了采集到所有的测量结果，多个传感器需要在结构上移动。这是个问题，特别是对轻质结构而言。解决这个问题的一个办法是，在结构上安装上所有的加速度计，即使每次仅测量一少部分。另一种方法是，在还没有测到的位置上加上哑元加速度计质量块；这样可以消除移动质量的影响。

 

Another difference that can result is due to the shaker/stinger effects. Basically, the modes of the structure may be affected by the mass and stiffness effects of the shaker attachment. While we try to minimize these effects, they may exist. The purpose of the stinger is to divorce the effects of the shaker from the structure. However, on many structures, the effects of the shaker attachment may be significant. Since an impact test does not suffer from these problems, different results may be obtained.

另一个差别是由激振器/推力杆的影响引起的。从根本上讲，结构的模态可能会受到质量和激振器连接装置的刚度效应的影响。尽管我们尽力减少这种影响，但它们可能存在。推力杆的目的是从结构上分离激振器的影响。但是在很多结构上，激振器连接装置的影响可能比较显著。因为锤击试验不受这些问题的不良影响，那么有可能得到不同的结果。

 

So while theory says that there is no difference between a shaker test and an impact test, there are some very basic practical aspects that may cause some differences. I hope this clears up this question.

尽管理论上讲激振器试验和锤击试验之间没有什么差别，但某些非常基本的实际问题导致它们之间可能存在某些差别。我希望本文的讨论澄清了这个问题。