Estimation of measurement errors in orthotropic elastic moduli determined from natural frequencies

Orthotropic elastic moduli of composite structures can be identified by nonlinear least squares fit between measured and computed natural frequencies. However, due to measurement errors contained in the measured natural frequencies and mode shapes, the process of elastic moduli identification is error-prone. This paper proposes an efficient method to estimate the errors in the elastic moduli caused by the measurement errors in the natural frequencies. The method utilizes an efficient semi-analytic expression of the sensitivities of the eigenvalues with respect to the orthotropic elastic moduli. First, the first-order approximation of the analytic sensitivity of orthotropic elastic moduli with respect to the measurement errors is introduced. The approximation is then used to estimate the variability of the identified elastic moduli due to the measurement errors. It is shown that the aspect ratio of the test specimen greatly affects the standard deviation of the identified elastic moduli. Second, using the first-order approximation, the effects of aspect ratio of the test specimen as well as the values of the elastic moduli are further investigated. Based on the results of numerical experiments, guidelines for the dimension of the test specimen for the elastic moduli identification are proposed.