Stochastic prediction of natural frequencies of laminated composite beams by using a high-order statistical moment based approach

Abstract

Statistical Moment (SM) based modelling is a quite straightforward approach in stochastic modelling of uncertain structures. However, the method still has deficiencies including determination of SMs of natural frequencies of vibratory structures, and it has not been tested yet for realistic structures. This study aims such verification by employing high-degree statistical moments in stochastic equations. In this respect, SM approach is applied for two different uncertainty cases. In the first case, uncertain parameters are experimentally reproduced from the batch of laminated composite beams. Then, those uncertainties are fed to SM equations used in finite element model to obtain descriptive statistical quantities (mean, variance, skewness, and kurtosis) of stochastic natural frequencies. Next, Pearson model is utilized to obtain probability density function of the natural frequency by using standardized SMs. Beside this, uncertain fundamental natural frequency of fifty samples of composite beams is measured by experimental modal tests. All SM based predictions and modal test results are also compared with numerical Monte Carlo Simulations. The latter case examines composite beams having nonnormal uncertain thickness. Since the results are in good harmony with each other, it is concluded that high-order SM based approach may effectively be used in uncertainty modelling of realistic structures.