Abstract
Implementing collinear wave mixing techniques with numerical methods to detect acoustic nonlinearity due to damage and defects is of vital importance in nondestructive examination engineering. However, numerical simulations in existing literatures are often limited due to the compromise between computational efficiency and accuracy. In order to balance the contradiction, spectral finite element (abbreviated as SFE) with 3 × 3 and 8 × 6 nodes is developed to simulate collinear wave mixing for 1D and 2D cases in this study. The comparisons among analytical solutions, experiments, finite element method (FEM), and spectral finite element method are presented to validate the feasibility, efficiency, and accuracy of the proposed SFEs. The results demonstrate that the proposed SFEs are capable of increasing computational efficiency by as much as 14 times while maintaining the same accuracy in comparison with FEM. In addition, five 3 × 3 nodes’ SFEs or one 8 × 6 nodes’ SFE per the shortest wavelength is sufficient to capture mixing waves. Finally, the proposed 8 × 6 nodes’ SFE is recommended for collinear wave mixing to detect damage, which can offer more accuracy with similar efficiency compared to 3 × 3 nodes’ SFE.
Highlights
Wave mixing techniques with noncollinear [1, 2] and collinear [3,4,5,6] incident waves have been used to detect the change of material nonlinearity caused by plasticity and fatigue damage
Two types of spectral finite elements are developed to simulate collinear wave mixing for damage detection
That the proposed SFEs could be viable numerical methods to simulate collinear wave mixing for damage detection
Summary
Wave mixing techniques with noncollinear [1, 2] and collinear [3,4,5,6] incident waves have been used to detect the change of material nonlinearity caused by plasticity and fatigue damage. It is necessary to simulate collinear wave mixing with numerical methods, which are the extension and supplement to the analytical solutions and the experiments. Finite element method requires strict rules for spatial and temporal discretization to study the interaction of waves, which can cause numerical problems in the cases of high frequencies and great dimensions [20,21,22]. The orthogonal polynomialsbased spectral finite element method [24,25,26] is much more suitable for analyzing wave propagation in structures with complex geometry. Rekatsinas et al [34] developed a time-domain spectral finite element for improving the efficiency of numerical simulations of guided waves in laminated composite strips. Two types of spectral finite elements are developed to simulate collinear wave mixing for damage detection. The comparison between two types of spectral finite elements is investigated by considering the contradiction between accuracy and efficiency
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