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1、MODAL SPACE - IN OUR OWN LITTLE WORLD模态空间-在我们自己的小世界中Pete Avitabile著 westrongmc译Biltii* bliobus hBfvs 口帀日thirl aniline- canCculd yfiu uc口Idin modal analysi s For mr?hli/Jlrufjjyji By .LfrA-e A vitshilc 加芒山加创电価匿IWWW-rikllN人邮可尉爛. E艇II_说来有点话用d HwiZkeCould you explain modal analysis for me?Well.it will t
2、ake a little bit but heres one that anyone can understand.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 explain modal analysis in simple terms so anyone can understand it. In a nutshell, we could say that modal analysis is a process whereby we describe a structure in terms of
3、 its natural characteristics which are the frequency, damping and mode shapes - its dynamic properties. Well thats a mouthful so lets explain what that means. Without getting too technical, I often explain modal analysis in terms of the modes of vibration of a simple plate. This explanation is usual
4、ly useful for engineers who are new to vibrations and modal analysis.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。Lets consider a freely supported flat plate. Lets apply a con
5、stant force to one corner of the plate. We usually think of a force in a static sense which would cause some static deformation in the plate. But here what I would like to do is to apply a force that varies in a sinusoidal fashion. Lets consider a fixed frequency of oscillation of the constant force
6、. We will change the rate of oscillation of the frequency but the peak force will always be the same value - only the rate of oscillation of the force will change. We will alsomeasure the response of the plate due tothe excitation with an accelerometer attached to one corner of the plate.考虑一个自由支撑平板，
7、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的平板响应。时间 time不斷增加彊葱連率 increasing rate ot asdllationWWW CMIMAVIIl. CE1MNow if we measure the response on the plate we will notice that the amplitude changes as we change the
8、rate of oscillation of the input force. There will be increases as well as decreases in amplitude at different points as we sweep up in time.This seems very oddsince we are applying a constant force tothe system yet the amplitude varies dependingon the rate of oscillation ofthe input force. But this
9、 is exactly what happens - the response amplifies as we apply a force with a rate of oscillation that gets closer and closer to the natural frequency (or resonant frequency) of the system and reaches a maximum when the rate of oscillation is at the resonant frequency of the system. When you think ab
10、out it, thats pretty amazing since I am applying the same peak force all the time - only the rate of oscillation is changing!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
11、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！This time data providesvery useful information. But if we take the time data and transform it to the frequency domain using the Fast Fourier Transform then we can compute something called the frequency response function. Now there aresome very interesting items to
12、 note. We see that there are peaks in this function which occur at the resonant frequencies of the system. Nowwe notice that these peaks occur at frequencies where the time response was observed to have maximum response corresponding to the rate of oscillation of the input excitation.这个时域数据提供了非常有用的信
13、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。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。Now if we overlay the time trace with the frequency trace what we will notice is that the frequency of oscillation at the time at which the time trace reaches its maximum value corresponds to the
14、frequency where peaks in the frequency response function reach a maximum. So you can see that we can use either the time trace to determine the frequency at which maximum amplitude increases occur or the frequency response function to determine where these natural frequencies occur. Clearly the freq
15、uency response function is easier to evaluate.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 amazing how the structure has these natural characteristics. Well, the deformation patterns at these natural f
16、requencies also take on a variety of different shapes depending on which frequency is used for the excitation 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 happens to the deformation pattern on the structure at each one of these natural frequencies. Lets place 45 evenly distributed accelerometers on the plate and measure the amplitude of the response of the
