A comparative survey of energy and finite element methods in plate vibration

Includes bibliographical references (pages 206-221)Approximate methods for analyzing the vibration of\ud plates are considered in this project. Classical energy\ud methods, employed for the purpose of obtaining\ud approximations to the natural frequencies and modes, are\ud the subject of Part One. These techniques are the\ud Rayleigh quotient, the Rayleigh-Ritz method, and the\ud Galerkin method. Basic theory and derivations are\ud presented and the interrelationships of the techniques\ud demonstrated. The specific problem of a thin square plate\ud clamped on all edges is employed as the vehicle through\ud which the methods are investigated. Rayleigh-Ritz\ud analyses are performed utilizing two types of coordinate\ud functions and numerical procedures: in the first, static\ud beam shapes are used and the numerical computations are\ud undertaken on a hand calculator; the second entails \ud employing beam modes, and utilizing a main frame\ud computer. Part Two consists of a comprehensive study and\ud literature survey of finite-element formulations/tecm1iques\ud in plate analysis, with particular emphasis on plate\ud vibration.\ud Classical energy techniques are found to be expedient\ud for the purpose of obtaining estimates of the lower\ud frequencies by Rayleigh's quotient utilizing beam modes as\ud coordinate functions. Rayleigh-Ritz analyses performed\ud with identical functions failed to produce gains in accuracy\ud commensurate with the additional labor necessary.\ud More complex problems, for which implementation of the\ud classical methods is impractical, require the use of more\ud versatile procedures such as the finite element method.\ud The survey of Part Two provides information on the\ud developments in, and pertinent aspects of, the finite\ud element method as used in plate analysis