Indirect stability of a 2D wave-plate coupling system with memory viscoelastic damping

Peipei Wang; Yanting Wang; Fei Wang; Peipei Wang; Yanting Wang; Fei Wang

doi:10.3934/math.2024962

AIMS Mathematics

2024, Volume 9, Issue 7: 19718-19736. doi: 10.3934/math.2024962

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Research article

Indirect stability of a 2D wave-plate coupling system with memory viscoelastic damping

1.
School of Mathematics and Statistics, Taiyuan Normal University, Jinzhong, Shanxi 030619, China
2.
School of Basic Education, Beijing Institute of Graphic Communication, Beijing 102600, China

Received: 22 April 2024 Revised: 03 June 2024 Accepted: 07 June 2024 Published: 17 June 2024
MSC : 35B37, 35L55, 74D05, 93D15

We performed a stability analysis of a 2D wave-plate coupling system equipped with memory viscoelastic damping. The study highlights the unique functionality of the damping mechanism, which operates indirectly and exclusively within either the wave or plate subsystem. The opposing subsystem receives dissipative signals indirectly through the coupling component. The primary objective of this study was to determine whether the indirect memory damping is sufficient to ensure the overall stability of the coupled system. To address this question, a frequency domain analysis was employed to establish explicit decay rates of the coupled system. Notably, a polynomial decay rate is observed when the memory damping is applied solely to either the plate or wave subsystem, which provides a conclusive answer to the posed question.
- wave-plate coupled system,
- infinite memory,
- frequency domain analysis,
- multiplier method
Citation: Peipei Wang, Yanting Wang, Fei Wang. Indirect stability of a 2D wave-plate coupling system with memory viscoelastic damping[J]. AIMS Mathematics, 2024, 9(7): 19718-19736. doi: 10.3934/math.2024962

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Abstract

We performed a stability analysis of a 2D wave-plate coupling system equipped with memory viscoelastic damping. The study highlights the unique functionality of the damping mechanism, which operates indirectly and exclusively within either the wave or plate subsystem. The opposing subsystem receives dissipative signals indirectly through the coupling component. The primary objective of this study was to determine whether the indirect memory damping is sufficient to ensure the overall stability of the coupled system. To address this question, a frequency domain analysis was employed to establish explicit decay rates of the coupled system. Notably, a polynomial decay rate is observed when the memory damping is applied solely to either the plate or wave subsystem, which provides a conclusive answer to the posed question.

References

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