A New Theory of Elastic Sandwich Plates—One-Dimensional Case

Abstract

Abstract A new flexural theory of isotropic elastic sandwich plates is deduced from the theory of elasticity. The one-dimensional case is presented in this paper. The theory includes the effects of transverse-shear deformation and rotatory inertia in both the core and faces of the sandwich, and no limitation is imposed upon the magnitudes of the ratios between the thicknesses, material densities, and elastic constants of the core and faces of the sandwich. The method used is an extension of one due to Mindlin [1], and the results reduce to those of his for the corresponding homogeneous plates as special limiting cases. A final equation also may be simplified and reduced to the corresponding results of Reissner [2], Hoff [3], and Eringen [4] for the bending of ordinary sandwich plates that have thin faces. Results of the theory are applied to the problem of bending of a cantilever plate subjected to load at the unsupported end and to the problem of propagation of straight-crested waves in an infinite plate.