AI-driven adaptive vibration control in smart plate systems: a sustainable approach for next-generation sports...

The current paper proposes an AI-based method for the vibration control of smart plate systems. The application is set for next-generation sports engineering, where performance enhancement is the main goal. The system consists of a core of coarse aggregate ultra-high-performance concrete (CA-UHPA) and piezoelectric face sheets, which are mounted on an elastic foundation. The properties of the material composite are foreseen based on the Halpin-Tsai models and the law of mixtures. Looking into the system's dynamic performance in a very thorough way is done using the quasi-3D theory having four variables. This theory gives the opportunity for the full consideration of the distribution of transverse shear strains and stresses throughout the plate thickness. The governing equations of the resonant response are derived by employing the concept of piezoelectricity together with Hamilton's energy principles. The elastic foundation is analyzed using both Winkler and Pasternak coefficients, thereby allowing the interaction of the plate and its support substrate to be included. The solution is achieved through using the physics-informed neural networks (PINNs) technique, which not only accurately and efficiently replaces the conventional Legendre Polynomial Expansions with deep neural networks (DNNs) for more computational efficiency and accuracy but also doubles the legacy of AI-powered methods in terms of real-time system adaptability and optimal vibration control under changing scenarios. A DNN-based verification process assists in obtaining and confirming the trustworthiness of the results. This research marks above all and the first time as a very promising new direction in the smart systems vibration control area in sports, and it is highly anticipated that the new development will have a positive impact on the performance and durability optimization of advanced sports equipment. The introduced method embodies a patent-driven technology leap in vibration control, where AI and new materials join forces to solve challenging problems.