Work

Exponential Stability of a Kirchhoff Plate Equation with Structural Damping and Internal Time Delay

Year: 2024

Type: article

Abstract: In this manuscript, we investigate the exponential stability of a Kirchhoff plate equation with free boundary conditions in a bounded domain of R2. First, we consider the case where the model is subjected only to structural damping and, using the energy method, we prove the exponential decay of the energy associated with this model. Second, we consider the case where structural damping with a linear internal time delay term is applied, and we use the same technique to derive the exponential stability of the new model. Finally, we examine the scenario where the model is governed by structural damping with an added fractional time delay term and, by constructing an appropriate Lyapunov function, we show that the energy associated with the system is exponentially stable. This work improves upon prior results concerning the Kirchhoff plate equation with frictional damping, where exponential stability could not be achieved.

Source: Symmetry

DOI: 10.3390/sym16111427

Authors: Zayd Hajjej, Hongwei Zhang

Institutions: King Saud University, Henan University of Technology

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,728

Funder: King Saud University