Vibration of plates

The vibration of plates is a special case of the more general problem of mechanical vibrations. The equations governing the motion of plates are simpler than those for general three-dimensional objects because one of the dimensions of a plate is much smaller than the other two. This permits a two-dimensional plate theory to give an excellent approximation to the actual three-dimensional motion of a plate-like object.

For the construction machine, see plate compactor.

There are several theories that have been developed to describe the motion of plates. The most commonly used are the Kirchhoff-Love theory and the Uflyand-Mindlin. The latter theory is discussed in detail by Elishakoff. Solutions to the governing equations predicted by these theories can give us insight into the behavior of plate-like objects both under free and forced conditions. This includes the propagation of waves and the study of standing waves and vibration modes in plates. The topic of plate vibrations is treated in books by Leissa, Gontkevich, Rao, Soedel, Yu, Gorman and Rao.

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