A Higher-Order Shear Deformation Model of a Periodically Sectioned Plate

Abstract

This paper develops a higher-order shear deformation model of a periodically sectioned plate. A parabolic deformation expression is used with periodic analysis methods to calculate the displacement field as a function of plate spatial location. The problem is formulated by writing the transverse displacement field and the in-plane rotations as a series solution of unknown wave propagation coefficients multiplied by an exponential indexed wavenumber term in the direction of varying structural properties multiplied by an exponential constant term in the direction of constant structural properties. These expansions, along with various structural properties written using Fourier summations, are inserted into the governing differential equations that were derived using Hamilton's principle. The equations are now algebraic expressions that can be orthogonalized and written in a global matrix format whose solution is the wave propagation coefficients, thus yielding the transverse and in-plane displacements of the system. This new model is validated with finite-element theory and Kirchhoff plate theory for a thin plate simulation and verified with comparison to experimental results for a 0.0191 m thick sectional plate.