Nonlinear frequency prediction and uncertainty analysis for fully clamped laminates by using a self-developed multi-scale neural networks system

To improve design accuracy and reliability of structures, this study solves the uncertain natural frequencies with consideration for geometric nonlinearity and structural uncertainty. Frequencies of the laminated plate with all four edges clamped (CCCC) are derived based on Navier’s method and Galerkin’s method. The novelty of the current work is that the number of unknowns in the displacement field model of a CCCC plate with free midsurface (CCCC-2 plate) is only three compared with four or five in cases of other exposed methods. The present analytical method is proved to be accurate and reliable by comparing linear natural frequencies and nonlinear natural frequencies with other models available in the open literatures. Furthermore, a novel method for analyzing effects of mean values and tolerance zones of uncertain structural parameters on random frequencies is proposed based on a self-developed multiscale feature extraction and fusion networks (MFEFN) system. Compared with a direct Monte Carlo simulation (MCS), the MFEFN-based procedure significantly reduces the calculation burden with a guarantee of accuracy. Our research provides a method to calculate nonlinear natural frequencies under two boundary conditions and presented a surrogate model to predict frequencies for accuracy analysis and optimization design.