If you perform a Modal analysis, it will reveal what frequencies the structure can vibrate at, and what shape those vibrations will take. To do this, the correct mass and stiffness of the structure must be used. That is why you will get a different natural frequency when the pipe is filled with air than when it is filled with liquid.
After you have done a Modal analysis, you can add on a Harmonic Response analysis. That will tell you the amplitude of the vibration everywhere on the structure when a sinusoidal force or moment or pressure load is applied somewhere on the body. The Harmonic Response analysis will show you how the structure vibrates as the sinusoidal load sweeps from a low frequency to a high frequency. An example of that is a pump with an impeller or rotor that has some small unbalance. As the pump RPM changes, the structure will vibrate with a small amplitude until the RPM reaches one of the natural frequencies found in the Modal analysis, then the amplitude will grow much larger.
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