Deep neural network–based mechanical modeling of nonlinear vibration behavior in porous GPL-reinforced plates with cut-outs

This paper introduces a deep learning-based surrogate model based on predicting the nonlinear vibration behaviors of platelets of porous nanocomposites reinforced with graphene platelets (GPLs) with central cut-outs. Conventional numerical approaches can provide precision but are too slow, particularly when dealing with high dimensional parametric analysis, or in real time. To overcome this shortcoming, an artificial neural network (ANN) surrogate model is formulated to effectively learn the complicated nonlinear interactions among design variables, such as plate geometry, GPL distribution patterns, reinforcement volume fractions, and porosity, and modal frequencies. Hamilton principle is used to obtain the motion equations of the reinforced plates of the porous GPL nanocomposite, where von Kármán geometric nonlinearity and Mindlin plate theory are incorporated to include both bending and shear effects. The plate with a central cut-out is divided into sub-domains to find vibration solutions whereby orthogonal polynomials are used to meet the geometric boundary conditions of each sub-domain. Lastly the continuity conditions are imposed and the Rayleigh-Ritz method is used to calculate the natural frequencies, which only gives an efficient and accurate solution strategy to the nonlinear vibration analysis. The model is also verified to agree with the finite element simulation in ABAQUS with the errors of less than 3%. It is shown that parametric analyses that incorporate GPL reinforcement clearly show that the distribution of vibrational frequencies is strongly enhanced by the presence of GPL reinforcement and that porosity decreases the frequencies of vibrations. The proposed surrogate modeling model offers a valuable low cost predictive method of vibration analysis which can easily optimize designs, quantify uncertainties and may be used in real-time structural health monitoring of complex nanocomposite systems.