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Investigation of Non-axisymmetric Lamb Wave in an Elastic Plate with Free Boundaries

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Abstract

Purpose

Lamb wave is widely used in damage detection and structural health monitoring of plate-like structures. In the current stage, the propagation of non-axisymmetric circular crested Lamb has not been theoretically solved. Therefore, it is essential to find its exact solutions.

Methods

The displacement expressions and frequency equations are derived through three-dimensional elastic theory using Helmholtz conversion. Numerical simulations and experiments are conducted on plates for verification of theoretical results.

Results

Both axisymmetric and non-axisymmetric waves are obtained from the governing equation with free boundary conditions. Lamb wave travels along the radial direction and holds as a standing wave in circumferential and longitudinal directions. The displacement field is expressed with Bessel functions in the radial direction and trigonometric functions in circumferential and longitudinal directions. Two families of Lamb wave modes are generated, which are identified by radial wavenumber and circumferential order. The amplitudes of displacements decrease with the propagation distance increases, and the circumferential distributions of displacements are affected by the circumferential order. Results obtained from simulation and experiment provide good verification for theoretical predictions.

Conclusions

The analytic solutions are presented in non-axisymmetric problems for circular crested Lamb wave in this paper, which provides a theoretical foundation for further investigation of Lamb wave propagation in plates.

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Acknowledgements

In this research work, Dalian Innovation Foundation of Science and Technology (2018J11CY005) and the State Key Laboratory of Structural Analysis for Industrial Equipment (S22303) are gratefully acknowledged.

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Authors and Affiliations

  1. School of Urban Construction, Yangtze University, Jingzhou, 434023, China

    Kai Zhou

  2. State Key Laboratory of Structure Analysis of Industrial Equipment, Department of Engineering Mechanics, Dalian University of Technology, Dalian, 116024, China

    Yanhong Guan, Quanquan Zhang, Yajing Wang & Xinsheng Xu

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  1. Kai Zhou
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  2. Yanhong Guan
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  3. Quanquan Zhang
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  4. Yajing Wang
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Correspondence to Xinsheng Xu.

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Zhou, K., Guan, Y., Zhang, Q. et al. Investigation of Non-axisymmetric Lamb Wave in an Elastic Plate with Free Boundaries. J. Vib. Eng. Technol. 11, 3293–3305 (2023). https://doi.org/10.1007/s42417-022-00749-9

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  • DOI: https://doi.org/10.1007/s42417-022-00749-9

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