Dynamic and frequency responses of the FG nanopipe using deep neural network and nonlocal strain/stress gradient theory

Abstract

This research introduces physics-informed supervised neural networks to predict the vibration behavior of nano-structures. In this regard, data-driven solution and data-driven discovery are presented to solve problems involving the determination of natural frequencies. Equations of motion are derived employing Hamilton’s principle for bi-directional functionally graded (FG) concrete nanopipe and solved with the aid of the discrete singular convolution-integrated method (DSC-IM). For modeling the current nanostructure, an exact size-dependent theory called nonlocal strain/stress gradient theory is presented. In this work, the structure is made of concrete materials, which vary exponentially in both thickness and axial directions. Further, a parametric study is conducted to investigate the effects of the FG power index in each direction, length to width ratio, and size-dependent parameters on the frequency of the bi-directional FG concrete nanopipe. By comparing the current results with the outcomes of the deep neural network, and open sources in the literature, the outcomes are verified. For future research, the outputs of this article can be used in the handbook of the nanostructures made of concrete materials.