Other causes of vibration. The seal is vibrating in harmony with some rotating component. The same thing that causes a rear view mirror to vibrate in an automobile. Operating the pump at a critical speed. Watch out for this problem in variable speed and pulley driven pumps.
Gases Dry running applications.
Too high a face load. Using unbalanced seals. Face load has changed because of temperature growth or impeller adjustment. You are using a high friction face combination. Often occurs if you use two hard faces.