Learning Forum

[deepesh.p.gurdasani]

After performing Harmonic analysis, we get a frequency response (Amplitude v. freq. and phase change graph). Why is there a phase change when amplitude reaches peak? what happens there exactly when amplitude reaches peak and causes 180 degree phase change. If someone can explain me a bit logically (like by giving some example of shaft, cantilever plate or something) THAN using formulae?

Thanks 

[peteroznewman]

Get a long spring and a heavy mass hanging from it where the natural frequency is about 1 Hz. That means the mass goes through a cycle of down, up, down in about 1 second. Hold the spring in your hand and let the mass hang.

If you move your hand slowly up and down at a fixed amplitude, taking about 5 seconds for a cycle, the mass follows your hand, just slightly lagging behind.  When your hand is at the top of its travel and starts heading down, the mass is also almost at the top if its travel and will head down momentarily. The motion of your hand and the mass are out of phase by -5 degrees. The amplitude of the mass is about equal to the amplitude of your hand.

Now move your hand up and down at 0.5 Hz, taking about 2 seconds for the cycle. The mass is now lagging significantly behind your hand and is out of phase by -45 degrees.

Move your hand up and down at 1 cycle per second. The mass is now moving out of phase by -90 degrees. That means that when your hand reaches the top of its cycle and starts heading down, the mass is at the center of its travel heading up. The amplitude of the mass becomes a maximum. The size of the maximum depends on the damping.

Now move your hand up and down at 2 Hz taking 1/2 second for the cycle. The phase is -135 degrees. Your hand reaches the top of its travel and starts downward while the mass is between the bottom of its travel and the halfway point still heading up.

As you cycle your hand faster and faster, the mass moves less and less. The phase begins to approach -180 degrees meaning when your hand is at the top heading down, the mass is at the bottom heading up.

This is summarized in the Amplification plot of a Single Degree of Freedom oscillator. The story above corresponds to inertial forcing which can be found in section 3.2 of the linked reference.

[deepesh.p.gurdasani]

If the natural frequency of the system is 1Hz as you have mentioned, the 180-degree phase should occur (as it occurs at resonance i.e when it vibrates at the natural frequency) when I am oscillating it at 1 cycle per second (You have mentioned 90-degree phase change at 1 cycle per second)? 

[peteroznewman]

When you get to resonance, the phase is -90 degrees.  As the forcing frequency goes further above resonance, the phase approaches 180 degrees.