Many structural parts such as aircraft components, boiler panels, industrial ducts, and machine parts are subjected to loading conditions that are conducive to vibration since they are in close proximity to reciprocating equipment or high fluid velocity. The mechanism of such plate vibration has been studied extensively in the last few decades. Numerous books and articles have been written dealing extensively with this topic. Leissa's book (Leissa 1969) gives solutions to extensive variety of plate geometries, boundary conditions, and material properties and serves as an excellent overall reference book. Another book by Gorman (Gorman 1982) develops detailed equations and solutions to a wide variety of rectangular plates. Other books on plate vibrations are also referenced in subsequent paragraphs.
In this chapter a brief description of the theory of the vibration of plates is presented for different plate configurations and boundary conditions to illustrate the general procedure for obtaining natural frequencies. The reader is encouraged to review the referenced books in this chapter for more in-depth treatment of the plate vibration problem.