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Exceptional points and perturbation dynamic response in PT-symmetric plates.

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Bibliographic Details
Title: Exceptional points and perturbation dynamic response in PT-symmetric plates.
Authors: Lai, A.1 (AUTHOR), Lim, C. W.2 (AUTHOR) bccwlim@cityu.edu.hk
Source: Proceedings of the Royal Society A: Mathematical, Physical & Engineering Sciences. 10/1/2025, Vol. 481 Issue 2323, p1-15. 15p.
Subjects: Perturbation theory, Symmetry (Physics), Critical point theory, Active noise & vibration control, Dynamic models
Abstract: Vibration systems with parity-time (PT) symmetry can exhibit a range of unique dynamical phenomena, thereby offering new insights for vibration control and related applications. Here, we establish a PT-symmetric plate dynamic model with gain and loss. The modal coalescence and dynamical evolution near the exceptional point (EP) are investigated, and the response to perturbations at the EP is also discussed. The result shows that as the parameters traverse the EP, the eigenvalues transition from purely real to complex conjugate, while the plate migrates from the PT-symmetric phase to the PT-symmetric broken phase. Owing to the spatial distribution of gain and loss, the PT-symmetric plate cannot form a conventional standing wave and instead supports a unique unidirectional wave mode. In addition, we investigate the response to both conservative and dissipative perturbations, revealing the remarkable sensitivity of plate at the EP, where the frequency response exhibits a square-root dependence on perturbation. This characteristic highlights the potential of PT-symmetric plates for high-precision sensing applications. This work not only deepens the understanding of modal transitions and energy-balance mechanisms in PT-symmetric two-dimensional structures but also offers a theoretical foundation for leveraging the high-sensitivity features of the EP in practical engineering design. [ABSTRACT FROM AUTHOR]
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Database: Engineering Source
Description
Abstract:Vibration systems with parity-time (PT) symmetry can exhibit a range of unique dynamical phenomena, thereby offering new insights for vibration control and related applications. Here, we establish a PT-symmetric plate dynamic model with gain and loss. The modal coalescence and dynamical evolution near the exceptional point (EP) are investigated, and the response to perturbations at the EP is also discussed. The result shows that as the parameters traverse the EP, the eigenvalues transition from purely real to complex conjugate, while the plate migrates from the PT-symmetric phase to the PT-symmetric broken phase. Owing to the spatial distribution of gain and loss, the PT-symmetric plate cannot form a conventional standing wave and instead supports a unique unidirectional wave mode. In addition, we investigate the response to both conservative and dissipative perturbations, revealing the remarkable sensitivity of plate at the EP, where the frequency response exhibits a square-root dependence on perturbation. This characteristic highlights the potential of PT-symmetric plates for high-precision sensing applications. This work not only deepens the understanding of modal transitions and energy-balance mechanisms in PT-symmetric two-dimensional structures but also offers a theoretical foundation for leveraging the high-sensitivity features of the EP in practical engineering design. [ABSTRACT FROM AUTHOR]
ISSN:13645021
DOI:10.1098/rspa.2025.0125