A new efficient nonlocal hyperbolic HSDT for mechanical vibration of porous FGM plates/nanoplates using Navier's method and artificial neural network prediction

Abstract

This paper introduces a new efficient hyperbolic high-order shear deformation theory (HHSDT) with a shape parameter (<i>Sₚ</i>) to study the vibration response of porous functionally graded material (FGM) plates and nanoplates. The shape parameter is optimized using a simple algorithm that adopts a neighbor selection strategy inspired by local-search algorithms, in order to obtain optimal frequencies. The equations of motion are derived using Hamilton’s principle, based on a 2D displacement field that contains only four unknowns, and are solved using Navier’s method. Nanoscale effects are considered through Eringen’s nonlocal elasticity theory. Moreover, MATLAB software is used to predict the fundamental frequencies using an artificial neural network (ANN), aiming to reduce computational cost. The effect of porosities on fundamental frequencies is studied using two types of uneven distributions (Type A and Type B). The novel Type B allows transitions between different distributions by controlling the parameter 𝑅. The current 2D-HHSDT provides more accurate results than many other 2D and quasi-3D HSDTs when compared with exact 3D solutions.