  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.
