Frictional moving load-induced dynamic response of a porous piezoelectric micro/nano plate with superficial parabolic discontinuity

Frictional moving load-induced dynamic response of a porous piezoelectric micro/nano plate with superficial parabolic discontinuity. The present paper aims to analyze the complex dynamic response of micro/nano-scale components through investigating the stress distribution within a Nonlocal Porous Piezoelectric Layer (NPPEL) of finite thickness. The study specifically focuses on quantifying the combined effects of material porosity, size-dependent elasticity, and geometrical surface imperfections when the layer is subjected to a load moving across its upper boundary. This comprehensive model provides a more realistic assessment of reliability for small-scale smart devices. The layer's constitutive behavior is modeled using Eringen's nonlocal elasticity theory to account for the essential size effects present at the micro/nano scale. The governing equations for the coupled porous and piezoelectric medium are derived, incorporating appropriate boundary conditions for a moving load. Crucially, the superficial parabolic discontinuity on the upper surface is handled analytically through a robust perturbation technique, allowing for the derivation of closed analytical forms for the resulting shear and normal stresses. The final solutions are then computed using Mathematica to illustrate the transient stress fields. Numerical results demonstrate that the nonlocal parameter is highly effective at amplifying the magnitude of the stresses, which is characteristic of the stiffening effect in nonlocal models. The depth and factor of the parabolic irregularity significantly amplify the stress concentrations at the interface, indicating a critical pathway for potential failure. Furthermore, the frictional coefficient of the moving load plays a non-linear role in dictating the shear stress distribution, providing crucial insight into contact mechanics at the nanoscale. The core novelty lies in the simultaneous analytical incorporation of nonlocal effects, porosity, and an arbitrary surface irregularity under dynamic moving load conditions-a combination highly relevant to microfabrication. The model is directly applicable to enhancing the design and performance assessment of MEMS/NEMS pressure sensors, ultra-thin piezoelectric energy harvesters, and other micro-electromechanical devices where surface quality and size effects dictate device lifespan and reliability.