模态分析报告地通俗解释

1、文档MODAL SPACE - IN OUR OWN LITTLE WORLD模态空间-在我们自己的小世界中Pete Avitabile 著 westro ngmc译辱画甌1阳WWWl4：i.llHAVIIlL r：tl MCould you expla in modal an alysis for me?Well.it will take a little bit but heres one that anyone can un dersta nd.你能为我解释模态分析吗?嗯说来有点话长，但下面的解释人人都可理解。Youre not the first one to ask me to ex

2、pla in modal an alysisin simpleterms so anyone can understand it. In a nutshell,we could say that modalan alysis is a process whereby we describe a structure in terms ofitsnatural characteristics which are the frequency, damping and modeshapes -its dynamic properties. Well thats a mouthful so lets e

3、xplain what that means. Without getting too technical,I often explain modal analysisin terms of the modes of vibrati on of a simple plate. This expla nati on is usually useful for engin eers who are new to vibrati ons and modal an alysis.请我用简单的概念来解释模态分析，以便任何人都可以理解它，你不是第一个人。 简言之，模态分析是一种方法，籍此，可以根据结构的频

4、率、阻尼和振型等固有 属性-其动态特性-来描述结构。这真够拗口的，那我们来解释这是什么意思。不 钻技术牛角尖，我经常用一个简单平板的振动模态来解释模态分析。对于刚接触 振动及模态分析的工程师们来讲，这种解释向来有益。Let s consider a freely supported flat plate. Lets apply a constant force to one corner of the plate. Weusually think of a force in a static sense which would cause some static deformation in

5、the plate. But here what I would like to do is to apply a force that varies in a sinusoidalfashion.Lets con sider a fixed freque ncy of oscillati on of the con sta nt force.Wewill change the rate of oscillation of the frequency but the peak force will always be the samevalue - only the rate of oscil

6、lation of the force will cha nge. We will also measure the resp onse of the plate due to the excitati on with an accelerometer attached to one corner of the plate.考虑一个自由支撑平板，施加常力于平板一角。我们通常从静态的意义上来看待 一个力，它在平板内引起某种静态变形。但这里我要做的是施加一个按正弦方式 变化的力，振荡频率固定的常力。我们将改变振荡频率，但不改变力的峰值-仅是力的振荡频率改变。另在平板一角安装一加速度计来测量激励引起

7、的平板响应。不斷增加扳荡速學 increasing rate of osdllaturWWW CMIM AVI B, COMNow if we measure the resp onse on the plate we will no tice that the amplitude cha nges as we cha nge the rate of oscillati on of the in put force. There will be in creases as well as decreases in amplitude at differe nt points as we swe

8、ep up in time. This seems very odd since we are appl ying a constant force to the system yet the amplitude varies depending on the rate of oscillati on of the in put force. But this is exactly what happe ns -the response amplifies as we apply a force with a rate of oscillation that gets closer and c

9、loser to the n atural freque ncy (or res onant frequency) of the system and reaches a maximumwhenthe rate of oscillation is at the resonant frequency of the system. Whenyou think about it, thats pretty amazing since I amapplying the samepeak force all the time - only the rate of oscillati on is cha

10、nging!如果现在测量平板响应，注意到当改变输入力的振荡频率时， 响应幅值也发生变 化。频率升高过程中，不同时刻点上，幅值有增也有减。这好像很奇怪，因为我们施加常力于系统，响应幅值却随输入力的振荡速率而变化。 但这确确实实发生 了 当施加的力的振荡速率越来越接近于系统固有频率（或共振频率）时, 响应增大，当振荡速率为系统固有频率时，响应达到最大值。想想看，这真令人 惊奇，因为我每时每刻都施加了相同幅值的力 -仅仅是振荡速率改变而已！frequencyWWW CHINJWIQ, CE1MThis time data provides very useful in formati on. But

11、 if we take the time data and tran sform it to the freque ncy doma in using the Fast FourierTran sform the n we can compute someth ing called the freque ncy resp onse fun cti on. Now there are some very in teresti ng items to n ote.We see thatthere are peaks in this function which occur at the reson

12、ant frequencies of the system. Now we notice that these peaks occur at frequencies where the time response was observed to have maximumresponse corresponding to the rate of oscillati on of the in put excitati on.这个时域数据提供了非常有用的信息。但是如果采集到时域数据，并利用快速傅 立叶变换将它变换到频域，则可以求得所谓的频响函数。现在有几点要关注：系 统共振频率处，这个函数上有峰值。

13、输入激励的振荡速率等于峰值频率的位置， 观察到了时域最大响应。WWW CHIN AVICUMNow if we overlay the time trace with the freque ncy trace what we will notice is that the frequency of oscillationat the time at which the timetrace reaches its maximumvalue corresponds to the frequency where peaks in the freque ncy resp onse fun cti on

14、 reach a maximum. So you can see that we can use either the time trace to determine the frequency at which maximum amplitude in creases occur or the freque ncy resp onse fun cti on to determ ine where these n atural freque ncies occur. Clearly the freque ncy resp onse fun ctio n is easier to evaluat

15、e.现在如果将时域波形跟频响图形叠加在一起，会注意到时域波形达到最大值时的 振荡频率与频响函数最大峰处的频率相一致。 所以，既可以利用时域波形来确定 幅值达到最大值处的频率，也可以用频响函数来确定固有频率何处发生。显然， 用频响函数更容易求。You thought it was pretty amaz ing how the structure has these n atural characteristics. Well, the deformati on patter ns at these n atural frequencies also take on a variety of d

16、ifferent shapes depending on which freque ncy is used for the excitati on force.结构为何具有这些固有属性，你感到大为惊奇。对了，在这些固有频率处，变形 形式也大为不同，依赖于激振力用哪个频率。Now lets see what happe ns to the deformati on pattern on the structure at each one of these n atural freque ncies. Lets place 45 eve nly distributed accelerometers

17、 on the plate and measure the amplitude of the resp onse of the plate with differe nt excitatio n freque ncies. If we were to dwell at each one of the freque ncies - each one of the n atural freque ncies - we would see a deformatio n patter n that exists in the structure. The figure showsthe deforma

18、ti on patter ns that will result whe n the excitation coincides with one of the natural frequencies of the system. Wesee that when we dwell at the first natural frequency, there is a first bending deformati on patter n in the plate show n in blue. Whe n we dwell at the sec ond n atural freque ncy, t

19、here is a first twisti ng deformati on patter n in the plate show n in red. When we dwell at the third and fourth n atural freque ncies, the sec ond bending and sec ond twisti ng deformati on patter ns are see n in gree n and mage nta, respectively. These deformati on patter ns are referred to as th

20、e modeshapes of the structure. (Thats not actually perfectly correct from a pure mathematical sta ndpo int but forthe simple discussi on here, these deformati on patter ns are very close to the mode shapes, for all practical purposes.)好了，我们来看一看，在每个固有频率处，结构上的变形形式是怎样的。在平板 上均布45个加速度计，测量不同激振频率的平板响应幅值。如果

21、在每个频率处 驻留一一每次一个固有频率一一可以观察结构上的变形形式。图中显示了 按某一阶系统固有频率激励时，得到的变形形式。在第一阶固有频率驻留时，平 板具有第一阶弯曲变形形式，如蓝色所示。在第二阶固有频率驻留时，平板具有 第一阶扭转变形形式，如红色所示。在第三、四阶固有频率驻留时，第二阶弯曲 和第二阶扭转变形形式如绿色和紫红色所示。这些变形形式称为结构的模态振型。（从纯粹数学角度讲，这不完全正确。但事实上，此处简单讨论起见，这些变形 形式非常接近于模态振型。）MfWW HIM AVIS. CUMNowthese natural frequencies and modeshapes occur

22、 in all structures that we design. Basically, there are characteristics that depend on the weight and stiff ness of my structure which determ ine where these n atural freque ncies and mode shapes will exist. As a desig n engin eer, I n eed to iden tify these freque ncies and know how they might affe

23、ct the resp onse of mystructure whena force excites the structure.Understanding the modeshape and how the structure will vibrate whe n excited helps the desig nengineer to design better structures. Now there is much more to it all but this is just a very simple explanation of modal analysis.你看，我们设计的

24、所有结构都具有这些固有频率和模态振型。从本质上讲，这些特性依赖于结构的质量和刚度，它决定了固有频率和模态振型存于何处。作为设 计工程师，需要识别这些频率，并且需要知道当力激励结构时，它们是如何影响 结构响应的。理解模态振型和受激结构如何振动， 将有助于设计工程师设计出更 优的结构。然而模态分析的内容很多，这只是一个非常简单的解释。Nowwe can better understand what modal analysis is all about - it is the study of the n atural characteristics of structures. Both the

25、 n aturalfreque ncy and mode shape (which depe nds on the mass and stiff ness distributions in my structure) are used to help design my structural system for noise and vibrationapplications. Weuse modal analysis to helpdesign all types of structures including automotive structures,aircraftstructures, spacecraft, computers, tennis rackets, golf clubs . the list just goes on and on.现在我们能够更好地理解模态分析是什么-它研究结构的固有特性。利用固有 频率和模态振型(依赖于结构的质量和刚度分布)帮助设计噪声