Hygrothermomechanical loading-induced vibration study of multilayer piezoelectric nanoplates with functionally graded porous cores resting on a variable viscoelastic substrate

Harnessing vibrations in multifunctional nanostructured plates is pivotal to next-gen microsystems but necessitates understanding scale effects under multifield loading. Investigated in this work are the forced and unforced vibrations of multilayered piezoelectric nanoplates supported on a variable viscoelastic medium and loaded hygrothermo-electromechanically with functionally graded porous (FGP) cores. The viscoelastic foundation is supposed to demonstrate non-linear changes in both stiffness and damping characteristics in the x-coordinate direction. The goal is to improve the accuracy of the results by using the nonlocal strain gradient theory (NSGT) and the third-order shear deformation assumption (TSDA), which include the effects of hardening and softening materials. The FGP core layer considers four states of porosity distribution patterns. These porosity distributions are expected to change in both the in-plane and thickness directions. The governing partial differential equations resulting from Hamilton's principle can be reduced to a system of algebraic equations by applying the Galerkin method. The parametric studies evaluate the effects of several factors, such as the initial electric voltage, viscoelastic medium parameters, moisture rise, temperature changes, porosity distributions, FG index, nonlocal and strain gradient features, and boundary conditions, on the vibration response. The novelty lies in the incorporation of advanced theories, such as the NSGT and TSDT, which capture size-dependent effects and material hardening/softening phenomena. Additionally, the consideration of four distinct porosity distribution patterns in the FGP core layer provides insights into the influence of porosity gradients on the dynamic response. The proposed model can guide the design and optimization of multifunctional nanostructured plates for applications in next-generation microsystems, energy harvesting devices, and smart structures.