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Natural Mode of Vibration

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Frequency Response

Time Stepping

Material Behavior

Dr. Layer 1.0
Exercise 8- Frequency Domain

Introduction

Introduction

### Background

The time required for an undamped system to complete one cycle of free vibration is the natural period of vibration of the system. We shall represent this as T in units of seconds. It is related to the natural circular frequency of vibration w with units of radians per second:

The natural cyclic frequency of vibration f which is implemented on the slider bar in Dr. Layer is given by the reciprocal value of T. This frequency represents the number of completed cycles per second. The units are Hertz (Hz). The frequency depends only on the mass and stiffness characteristics of the structure. This in effect means that the stiffer of two bodies with similar masses will posses a higher natural frequency and thus a shorter period. Conversely, the heavier of two bodies with the same stiffness will have a lower natural frequency. For linear systems these vibration properties are independent of the initial displacement and velocity.

### Objective

After this exercise you will understand how the input frequency affects the type of wave travel obtained.

### Things to Do

1. Open the Dr. Layer program. By default we get twelve layers. The top six layers are hardwired into the system with a very fast velocity. The bottom six layers are hardwired with a very slow velocity.

2. Starting with the set up above, move the cursor on the bottom left portion of the screen and push the time increment button to set up the wave motion.

3. Obtain the input period(T) from the plot box as the time it takes to complete one cycle.

4. Vary the frequency on the slider bar and obtain the new period.

5. The fast fourier transform plot can be obtained by pushing the plot box button and clicking on the existing plot box. You should obtain a box as shown below.

6. Change parameters to reflect the different wave speeds. What do you notice?

7. Try as many different combinations as possible and note the differences obtained in each combination.

### Observation

The type of wave motion obtained is different for each input frequency employed. The shape of the fast fourier transform plot is also a function of the input frequency and the wave speed of travel along the different media.