Statistical analysis and Neural Network Modeling of functionally graded porous nanobeams vibration in an elastic medium by considering the surface effects

The natural frequency of a clamped–clamped functionally graded porous (FGP) nanobeam is predicted in this study. Material distribution is considered based on monotonous, symmetric, and non-symmetric patterns in the thickness direction. This paper deals with governing equations of nanobeams based on third-order shear deformation beam theory in conjunction with nonlocal strain gradient theory (NSGT) and surface effects. Artificial neural network (ANN) is utilized to predict the effect of eight parameters including temperature gradient, residual surface stress, porosity distribution pattern, porosity parameter, nonlocal and material length scale parameters, and elastic and shear coefficients of Pasternak foundation on the fundamental frequency of FGP nanobeam. Different training methods are selected to simulate input and output dependency. Results show that the dependency of the natural frequency is inverse to the temperature gradient and nonlocal parameter in the sense that increasing these factors will decrease the natural frequency. Also, increasing the material length scale parameter grows the effect of the nonlocal parameter. Residual surface stress, material length scale, and Pasternak foundation parameters have a direct effect on the output and among them; the material length scale parameter has a more noticeable effect. Finally, it was found that by increasing the porosity parameter value, the diversity of natural frequency levels up drastically