A quantitative method for evaluating numerical simulation accuracy of time-transient Lamb wave propagation with its applications to selecting appropriate element size and time step

Xiang Wan; Guanghua Xu; Qing Zhang; Peter W Tse; Haihui Tan

doi:10.1016/j.ultras.2015.07.007

A quantitative method for evaluating numerical simulation accuracy of time-transient Lamb wave propagation with its applications to selecting appropriate element size and time step

Ultrasonics. 2016 Jan:64:25-42. doi: 10.1016/j.ultras.2015.07.007. Epub 2015 Jul 26.

Authors

Xiang Wan¹, Guanghua Xu², Qing Zhang³, Peter W Tse⁴, Haihui Tan⁵

Affiliations

¹ School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China; Department of Systems Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China. Electronic address: wx72420@163.com.
² School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China; State Key Laboratory for Manufacturing System Engineering, School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China. Electronic address: xugh@mail.xjtu.edu.cn.
³ School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China. Electronic address: zhangq@mail.xjtu.edu.cn.
⁴ Department of Systems Engineering and Engineering Management, City University of Hong Kong, Tat Chee Avenue, Kowloon, Hong Kong, China. Electronic address: meptse@cityu.edu.hk.
⁵ School of Mechanical Engineering, Xi'an Jiaotong University, Xi'an 710049, China. Electronic address: xy_thh@163.com.

PMID: 26315506
DOI: 10.1016/j.ultras.2015.07.007

Abstract

Lamb wave technique has been widely used in non-destructive evaluation (NDE) and structural health monitoring (SHM). However, due to the multi-mode characteristics and dispersive nature, Lamb wave propagation behavior is much more complex than that of bulk waves. Numerous numerical simulations on Lamb wave propagation have been conducted to study its physical principles. However, few quantitative studies on evaluating the accuracy of these numerical simulations were reported. In this paper, a method based on cross correlation analysis for quantitatively evaluating the simulation accuracy of time-transient Lamb waves propagation is proposed. Two kinds of error, affecting the position and shape accuracies are firstly identified. Consequently, two quantitative indices, i.e., the GVE (group velocity error) and MACCC (maximum absolute value of cross correlation coefficient) derived from cross correlation analysis between a simulated signal and a reference waveform, are proposed to assess the position and shape errors of the simulated signal. In this way, the simulation accuracy on the position and shape is quantitatively evaluated. In order to apply this proposed method to select appropriate element size and time step, a specialized 2D-FEM program combined with the proposed method is developed. Then, the proper element size considering different element types and time step considering different time integration schemes are selected. These results proved that the proposed method is feasible and effective, and can be used as an efficient tool for quantitatively evaluating and verifying the simulation accuracy of time-transient Lamb wave propagation.

Keywords: Cross correlation analysis; GVE (group velocity error); MACCC (maximum absolute value of cross correlation coefficient); Quantitative method; Simulation accuracy evaluation.