Wave responses in seismic FGM concrete nanobeam using deep neural network

In the current study, we investigate the vibration of a nano-scale beam structure composed of bi-directionally functionally graded concrete. We employ a dual approach, combining mathematical structural modeling with deep neural network analysis, to determine the natural frequency of the nanobeam. The concrete is assumed to be graded along the beam’s axis and transverse direction, following a power-law model.

We utilize Timoshenko beam theory (TBT) and nonlocal stress-strain gradient relations to describe the nanobeam’s displacement field. Hamilton’s principle is used to account for external forces and boundary conditions. A deep neural network is trained to predict the natural frequency with varying error margins.

The governing equations are solved using the differential quadrature numerical method, and the results are validated against existing literature. This work introduces novelties in three key areas: 1) a model for bi-FG concrete nanobeams under in-plane loading, 2).