On the Exponential Stabilization of the Nonlinear Rotating Body‐Beam System With a Boundary Infinite Memory of Type Angular Velocity: Theoretical and Numerical Results

Abstract

ABSTRACT This paper is concerned with the investigation of the effect of a boundary infinite memory term on the stability of the nonlinear rotating disk‐beam system. Assuming that infinite memory is of the angular velocity type, the minimal state approach is employed to handle the memory term. Under specific conditions on the memory kernel function and the physical parameters of the system, we demonstrate that the problem is well‐posed and its solutions are exponentially stable. In particular, the beam vibrations are suppressed, and the disk keeps rotating at a desired angular velocity, provided the latter remains bounded. Last but not least, using the Finite Volumes Method, a comprehensive numerical study validates the theoretical stability results.