An asymptotic theory for the motion of elastic plates

Abstract

Two dimensional theories for the vibrations of transversely isotropic elastic plates are derived without initially specifying the spatial dependence of the field variables on the thickness coordinate. This is accomplished by extending the method of asymptotic integration of the three dimensional elasticity equations to dynamic problems. The method consists of the expansion of all field variables and introduced length scales in terms of a small plate parameter. Substitution into the elastcity equations leads to field equations of various orders. The lowest order system of equations yields the simplest plate equations. Higher order systems introduce thickness effects.