Coupled aeroelastic–nanomechanical modeling of functionally graded piezoelectric tapered nanoplates used in sports equipment: results verification via a hybrid machine learning algorithm

Abstract

This work introduces a new coupled aeroelastic–nanomechanical theory for a class of materials, the functionally graded piezoelectric nanoplates that are considered for NEMS applications in the near future sports products. Nonlocal strain gradient theory (NSGT) and quasi-3D refined theory (Q3D-RT) are utilized to obtain the equations of motion for rectangular NEMS of varying thickness. The model covers several aspects, such as Von-Karman nonlinearity, nonlinear group and phase velocities, and the application of aerodynamic forces on the plates according to first-order piston theory. Nonlinear effects are captured by an iterative harmonic displacement representation, which also allows for the comprehensive description of the plate dynamics under the applied excitations. A hybrid machine learning algorithm employing fuzzy logic and deep neural networks (fuzzy-DNNs) is utilized to authenticate the model’s outcomes. With the help of the fuzzy-DNNs algorithm, the system’s nonlinear response characteristics, including the ratio of nonlinear group to phase velocity, are predicted with great efficiency, thereby providing solid validation for the model proposed. Furthermore, piezoelectric coupling in nanoplates is recognized as a factor for the enhancement of their mechanical performance, giving ideas about their usage in sports equipment where sensitivity, low weight, and high dynamic performance are important. The receipt of these results indicates a major breakthrough in the field of NEMS research, because up to now they have already revealed the essential contribution that nonlinear aeroelastic effects and electric interactions make to the formation of ultimate nanodevices. The research further proposes the theory-driven revolution of combining nanomechanics, piezoelectricity, and aeroelasticity as a way of producing new materials for the sports gear of the next generation.