Physics-informed neural networks: A deep learning framework for solving the vibrational problems

The provided paper considers the vibrations of viscoelastic sandwich disk reinforced by graphene nano-platelets (GPLs) filled viscoelastic concrete (GPLRVC) honeycomb core and face sheets via deep learning. The optimum values of the parameters involved in the fully connected neural network are determined through the momentum-based optimizer. The strength of the method applied in this study comes from the high accuracy besides lower epochs needed to train the multi-layered network. The honeycomb core would be manufactured by aluminum according to its great stiffness and lightweight. The mixture rule and modified Halpin–Tsai model have been involved in creating an efficient concrete material constant. By applying energy methods, the system's governing equations have been extracted and solved through Generalize Differential Quadrature (GDQ) technique. In the given research, Kelvin-Voigt viscoelasticity has been applied to model viscoelastic properties. The time-dependent deflection would be solved applying the fourth-order Runge-Kutta computational approach. Then, a parametric study has been conducted to analyze the influences of the external and internal radius ratio, thickness to length ratio of the concrete, hexagonal core angle, the GPLs' weight fraction, and the honeycomb core's thickness to internal radius ratio on the vibrations of the viscoelastic sandwich disk considering face sheet of FG-GPLRVC and honeycomb core.