Nonlinear Group and Phase Velocities in TD-FG Skew Plates as Bridge Structure Support Validated by Deep Neural Network Model

The purpose of this analysis is to examine the nonlinear group and phase velocities of three-dimensional functionally graded (TD-FG) skew plates. These skew plates can function as bridge supports for multistory buildings, while additionally utilizing advanced computational methods for the purposes of validation. Both shear and rotational inertia are taken into account with a higher-order shear deformation theory (HSDT) approach, allowing more precise modeling of thick structures during dynamic loads. The nonlinearities resulting from the material gradation and configuration of the skew plates are addressed through the harmonic balance method with an iterative solution procedure. This allows for the establishment and computation of the steady state solutions for periodic excitations. In addition, a deep neural network (DNN) architecture is proposed to provide model validation for more conclusive results. The DNN, trained on data from numerical simulations, allows for a data-driven method to check the accuracy of the predicted group and phase velocities. This machine learning model can be a valuable tool for cross-checking established analytical methods and offers verification of the reliability of the solution process and efficiency in finding it. Results are shown in velocity dispersion curves, where one can observe the effects of material gradation, plate geometry, and boundary conditions on the dynamic response of TD-FG skew plates. This research fundamentally builds understanding regarding wave propagation in complicated composite structures and offers a verified groundwork for the design and interpretation of bridge supports in engineering applications.