Free vibration of composite plates and identification of elastic properties

This paper deals an inverse vibration problem in which the elastic properties of composite materials are estimated from the measured modal characteristics of completely free plates. Approximate expressions are derived for estimating the six lowest natural frequencies of the plate. The validity of these formulas is verified using a Rayleigh-Ritz model with polynomial approximation functions in which the number of terms can be increased arbitrarily until convergence is achieved These formulas bring important insight into the problem and are used to calculate an accurate first estimate of the plate rigidities. The procedure developed for refining these estimates using the Rayleigh-Ritz model is shown to produce very accurate results and to be more efficient than previous methods. Several examples are presented and results are compared with those published by previous investigators. The approach can be readily extended to plates with other support conditions.