The nonlinear S0 Lamb mode in a plate with a linearly-varying thickness

Zhongtao Hu; Zhiwu An; Yuanyuan Kong; Guoxuan Lian; Xiaomin Wang

doi:10.1016/j.ultras.2018.11.013

The nonlinear S₀ Lamb mode in a plate with a linearly-varying thickness

Ultrasonics. 2019 Apr:94:102-108. doi: 10.1016/j.ultras.2018.11.013. Epub 2018 Nov 30.

Authors

Zhongtao Hu¹, Zhiwu An², Yuanyuan Kong¹, Guoxuan Lian³, Xiaomin Wang¹

Affiliations

¹ State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China.
² State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China; University of Chinese Academy of Sciences, Beijing 100049, China. Electronic address: anzhiwu@mail.ioa.ac.cn.
³ State Key Laboratory of Acoustics, Institute of Acoustics, Chinese Academy of Sciences, Beijing 100190, China.

PMID: 30563710
DOI: 10.1016/j.ultras.2018.11.013

Abstract

The aim of this paper is to investigate propagation characteristics and the generation mechanism of the nonlinear lowest-order symmetric Lamb mode (S₀) which propagates downslope in free elastic plates with slowly linearly varying-thickness. From theoretical analyses, in a low frequency-thickness product (fd) range, the S₀ mode is slightly dispersive, it is easy to generate, and it approximately satisfies the principle of the phase velocity matching. Therefore, if a S₀ mode is excited at a proper frequency in the low fd range, the amplitude of the second harmonic wave is linearly increasing in a certain propagating-distance, which is valuable for the practical NDE application of the second harmonic wave. Moreover, numerical simulations and experiments have been carried out to validate theoretical results. Our investigation of properties of the second harmonic wave can be applied to characterize and evaluate micro-structural damages in varying-thickness waveguides.

Keywords: Nonlinear Lamb wave; S(0) mode; Varying thickness plates.