A new random vibration response analysis method for laminates: Geometric nonlinearity and uncertainty are both involved for higher consistency with reality

To enable high-precision analysis and reliable design of laminates, a novel method is proposed for solving the random vibration response while accounting for geometric nonlinearity and structural uncertainty. The power spectral densities (PSDs) of deflection, velocity, and acceleration for a SSSS plate (indicating that all edges are simply supported) are derived using statistical linearization. In particular, the number of unknowns in the displacement field model of an SSSS-2 plate (where SSSS-2 denotes a simply supported plate with a free mid-surface) is reduced from five to three compared to conventional algorithms. This simplification reduces the complexity of the nonlinear equations and significantly improves computational efficiency. Furthermore, a novel framework was proposed, featuring a multiscale feature extraction, fusion, and learning network (MFEFLN). This network consists of three multiscale feature extraction blocks, one multiscale feature concatenation block, and one high-level feature fusion block. A dedicated network system was developed to analyze the influence of the mean values and tolerance zones of uncertain structural parameters on the random vibration responses. When predicting the same number of random response PSDs, the MFEFLN-based procedure demonstrates greater efficiency than direct Monte Carlo simulation (MCS) and superior accuracy compared to BP, GAN, LSTM, 2D CNN, and ADCNN methods. This research is beneficial for the design optimization and reliability guarantee of laminated structures by providing high-precision analysis results of the dynamic performance by covering the geometric nonlinearity and uncertainty that exist in actual products.