2023/11/09 by Ahmet Özer, Ozer, Ahmet Ozkan, Ibrahim Khalilullah +3
Engineering · Materials Science · Physics and Astronomy · #35E15 #65M06 #74S10 #74S20 #78-10 #93D15 #Analysis of PDEs (math.AP) #FOS: Mathematics #Magnetic Properties and Applications #Model Reduction and Neural Networks #Numerical Analysis (math.NA) #Optimization and Control (math.OC) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2311.05306
openalex publication_date 2023/11/09 · openalex created_date 2023/11/11 · openalex updated_date 2026/07/28
This study investigates a strongly-coupled system of partial differential equations (PDE) governing heat transfer in a copper rod, longitudinal vibrations, and total charge accumulation at electrodes within a magnetizable piezoelectric beam. Conducted within the transmission line framework, the analysis reveals profound interactions between traveling electromagnetic and mechanical waves in magnetizable piezoelectric beams, despite disparities in their velocities. Findings suggest that in the open-loop scenario, the interaction of heat and beam dynamics lacks exponential stability solely considering thermal effects. To confront this challenge, two types of boundary-type state feedback controllers are proposed: (i) employing static feedback controllers entirely and (ii) adopting a hybrid approach wherein the electrical controller dynamically enhances system dynamics. In both cases, solutions of the PDE systems demonstrate exponential stability through meticulously formulated Lyapunov functions with diverse multipliers. The proposed proof technique establishes a robust foundation for demonstrating the exponential stability of Finite-Difference-based model reductions as the discretization parameter approaches zero.