Abstract
Two-dimensional equations of successively higher orders of approximation for elastic, isotropic plates are deduced from the three-dimensional theory of elasticity by a series expansion in terms of simple thickness-modes for infinite plates. For each order of approximation from the zeroth up to the fourth, kinetic and strain energy densities, stress-strain relations and displacement equations of motion for both flexural and extensional vibrations are presented. Dispersion curves for real and imaginary as well as complex wave numbers in an infinite plate are explored in detail and compared with the solution of the Rayleigh-Lamb frequency equation from the three-dimensional theory.
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