Determination of Elastic Constants of Orthotropic Plates By A Modal Analysis/Method of Superposition

Abstract

The aim of the work reported here is to provide a single non-destructive test to determine the elastic constants of an orthotropic material by studying the free vibrations of a rectangular plate in completely free boundary conditions. After the experimental impulse technique to measure the natural frequencies of the plate has been presented, this paper deals with the development of an accurate numerical method to calculate these frequencies: the method of superposition, based on series expansions of the deformed plate shape and requiring the boundary conditions to be satisfied, in contrast to the Rayleigh-Ritz approximate technique. The equations derived by the method of superposition are incorporated into a computer designed to determine the five elastic constants of the material from the measured experimental natural frequencies of the completely free rectangular plate. In the following part of the paper, a few results are reported: first, the study of a glass plate validates the methodology employed by showing the expected isotropy of this material; second, the very weak orthotropy found for a laminated steel plate shows the sensitivity of the method; and finally the values of the two Young's moduli, the in-plane shear modulus and the two Poisson ratios calculated for a glass/epoxy plate are reported.