In a separate paper, the first two authors have described a method for deriving the elastic constants of an orthotropic composite material from resonance frequencies and mode shapes obtained in a modal analysis of a completely free plate. In this paper, the method is customized for isotropic materials. This much faster version, which presumes isotropy, is used to predict the elastic constants of square-plate specimens of aluminum and a nearly isotropic glass/polyester sheet molding compound (SMC). The results are compared to those from the full orthotropic method.
The paper examines the relative accuracies of the methods for obtaining frequencies. It also examines the effects on the predicted elastic constants of two different methods for simulating the free edge boundary condition: suspension by nylon filaments and placement on a soft cotton pad. The inverse method is used to obtain the properties of the SMC plate and of a rectangular graphite/epoxy plate cushioned on the cotton pad. The rectangular-plate graphite/epoxy results are compared to results for the same plate suspended by nylon filaments, and to those from the suspended square plate of the same material.
These results indicate that the method proposed by the authors has potential for rapidly and economically estimating the elastic constants of isotropic and orthotropic materials.