Nonlinear phase velocities in tri-directional functionally graded nanoplates coupled with NEMS patch using multi-physics simulation

The nonlinear phase velocities analysis of tri-directional functionally graded (FG) nanoplates is crucial for optimizing their performance as nano-electro-mechanical systems (NEMS). By understanding the nonlinear phase velocities of various wave modes within the nanoplate, engineers can accurately predict and enhance the efficiency of NEMS. This analysis allows for the precise tuning of the piezoelectric patches to capture vibrational energy more effectively, ensuring maximum energy conversion efficiency. Moreover, it helps in identifying the optimal placement and orientation of the piezoelectric patches, minimizing energy loss and enhancing the reliability and durability of the NEMS. Ultimately, this leads to more efficient utilization of ambient vibrations in airplanes, providing a sustainable power source for various onboard sensors and monitoring systems, contributing to reduced reliance on external power sources, and improved overall energy management. For this issue, for the first time, nonlinear phase velocity in the tri-directional functionally graded nanoplate coupled with a piezoelectric patch via COMSOL multi-physics simulation, physics-informed deep neural networks (PIDNNs), and mathematics simulation are presented. In the mathematics simulation domain, nonlocal strain gradient theory for modeling both the hardening and softening behavior of the current nanoplate is presented. The electromechanical coupling effect and the abrupt change in material properties at the interfaces will have a major influence on the mechanical performance of tri-directional functionally graded (TD-FG) nanoplate coupled with a piezoelectric patch if transverse shear deformations cannot be well modeled. Thereby, in the current simulation, a quasi-3D refined theory with 10 variables is presented. Also, for coupling the composite structure with the piezoelectric patch, compatibility conditions are considered. An analytical solution procedure is presented for solving the nonlinear partial differential equations of the current electrical system.