具有不同类型阻尼弱耦合板方程的间接镇定和最优衰减率

Abstract

Abstract:

This work is concerned with the stabilization and optimal decay rates of a weakly coupled (coupling through displacements) elastic plate system, where the damping (viscous damping, structural damping or Kelvin-Voigt damping) is actuated at only one of the two plates. The optimal polynomial decay rate is derived based on the frequency domain approach and detailed spectral analysis of the system operator. Moreover, the relationship between the optimal decay rates of the system and the order of damping is identified. Besides, an interesting phenomenon is found that the higher the order of indirect damping is actuated, the slower polynomial decay rate of the weakly coupled plate system achieves. Finally, some numerical simulations are presented to verify the theoretical results.

Key words: Coupled elastic plate, Indirect stabilization, Optimal polynomial decay, Spectral analysis, Frequency domain analysis

CLC Number:

O231.4

Han Zhongjie, He Yiheng, Zhao Zhixue. Indirect Stabilization and Optimal Decay Rates of Weakly Coupled Plates with Various Types of Damping[J].Acta mathematica scientia,Series A, 2023, 43(6): 1681-1698.

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References 38

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Indirect Stabilization and Optimal Decay Rates of Weakly Coupled Plates with Various Types of Damping

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