Dynamic stiffness formulation for the vibration response of functionally graded nanoplates considering the neutral surface position with microstructural defects

Abstract

In the present paper, the dynamic stiffness matrix of a functionally graded nanoplate (FG-nP) has been developed and used to carry out a vibration analysis. The nonlocal elasticity theory in conjunction with classical plate theory (CPT) has been used to drive the governing equations of motion using Hamilton’s principle. The nonlocal elasticity theory incorporates the length scale parameter, which can withhold the small-scale effect that is necessary for model FG-nP. The pioneer Wittrick–Williams algorithm is employed to evaluate the dynamic stiffness matrix. The property of the FG-nP has been calculated using the power law. The authenticity and efficacy of the present formulation have been ascertained using various validation studies. The accurate prediction of the effect of porosity inclusions on different volume fraction indexes, boundary conditions, and higher vibration modes has been reported. The influence of the nonlocal parameter, boundary conditions, various gradation techniques, and geometric parameters on vibration behavior has been extensively explored. The results show the versatility of the proposed approach in addressing small scaled complex engineering structures. This research significantly contributes to the understanding and analysis of functionally graded nanoplates, providing valuable insights for applications in aerospace, structural systems, sensors, actuators, and energy harvesting devices.