Measuring the Bending Stiffnesses of Orthotropic and Symmetric Laminates from Flexural Vibrations

Abstract

The paper develops an extensive analysis of the problem of determining the bending stiffnesses of orthotropic and symmetric laminates from flexural vibrations of rectangular plates with different boundary conditions consisting of clamped or free edges. Rayleigh’s approximation and Ritz method are considered for evaluating the flexural vibrations of plates. The experimental results and an analysis of the sensibility show clearly the tendency for the evaluation of the bending stiffnesses from the natural frequencies of the flexural vibrations of an orthotropic or symmetric plate to be an ill conditioned problem. It results that iterative procedures associated with Ritz method or with numerical method as finite element analysis cannot be used for evaluating the bending stiffnesses from the natural frequencies of a single plate in industrial applications. For orthotropic laminates, the paper shows how the Rayleigh’s approximation allows to overcome the problem of the divergence of the iterative processes. This approximation suggests another methods for evaluating the bending stiffnesses and their variations with the frequency. Next for symmetric laminates, the evaluation of the stiffnesses from the flexural vibrations of plates is implemented using the measurement of the mode shapes deduced from experimental modal analysis.