Vibrations of free plates: line symmetry; corresponding modes

Abstract

The normal modes of vibration of a plate with m lines of symmetry may be divided into 2 f classes, where f denotes the number of factors of m . The normal vibration patterns of a plate may be arranged on a diagram in which all classes of symmetry recur in every two rows (or one row for the circular plate) and in every m columns. The normal modes of vibration of plates correspond with one another. That is to say, every vibration pattern on one plate has a counterpart on every other plate. This is shown on the diagrams mentioned above by the fact that they all contain the same number of vibration patterns, and that patterns which occupy the same positions belong to the same mode of vibration on the circular plate. The principle of corresponding vibrations can be extended to plates of irregular shape. Combined vibrations must also conform to the symmetry of the plate.