### Modal AnalysisA Simple Viewpoint

So often people ask me exactly what is Modal Analysis all about.

Without getting too technical, I often explain Modal Analysis in terms of the modes of vibration of a simple plate.

Consider a simple, freely hung flat plate. A constant force will be applied to one corner of the plate but the frequency of the excitation will change in a sinusoidal fashion. As the frequency of the constant force changes, let's measure the response at a corner on the plate using an accelerometer.

If I measured the time response of the accelerometer, I notice that the level of amplitude of response changes as I change the frequency of oscillation. That seems odd since the level of excitation is constant - but this is exactly what happens. A typical time response is shown below.

Now this time response is very informative, but if I were to view this same data in the frequency domain, some other very interesting items can be noted. In order to view this data in the frequency domain, the Fast Fourier Transform will be used to convert the time data. A typical frequency response function (FRF) plot is shown below. The peaks in this plot correspond to the frequency of oscillation where the amplitude of response is greatest.

This can be easily seen if I overlay the time trace and the frequency trace together as shown below. As the amplitude of response in the time trace increases, the amplitude of the FRF also increases. These points of increased amplitude occur at the natural frequency of the system. The natural frequency of my structure depends on the mass and stiffness distributions in my structure. Looking at just one of these time traces provides useful information.

Now let's see what happens to the deformation pattern on the structure at each one of these natural frequencies. Let's place 45 evenly distributed accelerometers on the plate and measure the amplitude of the response of the plate when the excitation coincides with each of the four resonant frequencies at each of the peaks in the FRF. The figure below shows the deformation patterns that will result when the excitation coincides with one of the natural frequencies of the system.

If you would like to see each deformation pattern animated,
try each of the individual frequencies identified below.

Try the first frequency. Notice that the shape of deformation is a bending motion.

Try the second frequency. Notice that the shape of deformation is a twisting motion.

Try the third frequency. Notice that the shape of deformation is a second bending motion.

Try the fourth frequency. Notice that the shape of deformation is a second twisting motion.

The response of the structure is different at each of the different natural frequencies. These deformation patterns are called mode shapes. Now we can better understand what Modal Analysis is all about - it is the study of the natural characteristics of structures. Both the natural frequency (which depends on the mass and stiffness distributions in my structure) and mode shape are used to help design my structural system for noise and vibration applications. We use Modal Analysis to help design all types of structures including automotive structures, aircraft structures, spacecraft, computers, tennis rackets, golf clubs, ...

I hope this helps explain Modal Analysis for you.

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