PSI - Issue 45

Xianwen Hu et al. / Procedia Structural Integrity 45 (2023) 20–27 Hu, X., Liang, P., Ng, C.T., and Kotousov, A. / Structural Integrity Procedia 00 (2019) 000 – 000

25

6

4. Finite Element Model Validation 4.1. Experiment setup

One 1100×300×16 mm aluminium plate was used in the verification experiment. The plate has the same material properties and thickness as the FEM. Figure 6 schematically illustrates the experimental setup for the generation and measurement of edge waves on the aluminium plate. Firstly, the tonne-burst signal, which was the same as the signal in the FE simulation, was generated by a signal generator (NI PXle-1073). Then, the signal was amplified by an amplifier (Ciprian HVA-800-A) to ± 160 V. Next, the high-voltage signal was sent to a PZT (PI Ceramic GmbH c255) bonded on the top edge of the plate. The PZT has a diameter of 10 mm and a thickness of 0.5 mm. The distance between the centre of the PZT and the left edge of the plate was 450 mm and the distance between the centre of the PZT and the measurement point is 155 mm which is the same as the FEM. Next, the out-of-plane displacement at the measurement point was collected by the scanning laser vibrometer (Polytec PSV-400-M2-20). To enhance the quality of measured signals, reflective paint was evenly coated on the measurement area of the aluminium plate.

Fig. 6. Schematic diagram of the experimental setup

Fig. 7. Harmonics Response of Numerical and Experimental Data

4.2. Validation with harmonic responses Figure 7 compares the received response signal from nonlinear FE and the experimental measurements. In order to directly validate the nonlinear FEM, the data were normalised by their corresponding maximum peak amplitudes. The blue solid line and the red dotted line represent the experimental data and numerical data, respectively. Peaks appear in both experimental and numerical responses for primary waves at excitation frequency (f1), second harmonics at twice the excitation frequency (2f1), and other higher harmonics. In addition, the ratio of harmonic amplitudes in the numerical result is similar to that of the experimental result. Thus, although the simulation results do not perfectly match the reality, the use of subroutine VUMAT in ABAQUS/Explicit can provide a reasonable simulation of nonlinear edge wave behaviour. 5. Parametric Study This section presents a parametric study to investigate the effect of varying material nonlinearity on the edge wave’s nonlinear features. Stobbe (2005) experimentally measured the nonlinear material properties of the aluminium plate at different fatigue levels. He concluded that the third-order elastic constants change significantly during the early fatigue stage, while the second-order elastic constants remain unchanged. The experimentally measured third-order elastic constants of the aluminium plate are shown in Table 3. Therefore, three simulations were carried out in the parametric study with different sets of material properties of the aluminium plate at 0%, 40%, and 80% fatigue.