·Table of Contents ·Workshop - Guided Wave | Quantitative Guided Wave NDEJ. L. Rose, S. P. Pelts, Jian LiDepartment of Engineering Science and Mechanics The Pennsylvania State University 212 Earth & Engineering Science Building University Park, PA 16802 Contact |
Fig 1: Modeling statement of a guided wave striking an elliptical defect. |
Two different cases of an elastic field are considered: the first is for Lamb wave propagation modes and the second for a shear horizontal (SH) field. BEM results are presented for a 10 mm steel plate and elliptical wastage parameters of 2a=6.35 mm and various b values.
Sample phase and group velocity dispersion curve results are shown in Figure 2. Details of the computational process and explanations of dispersion curve generation and BEM development can be found in [1]. To illustrate the process of BEM utility for wave scattering in a wave guide, a sample problem of S0 mode impingement onto a series of different depth elliptical defects is illustrated in Figure 3. Even though reflected and transmitted modes are numerous including A0, S0, A1, S1, A2, S2, etc., whatever modes can exist at the incoming mode frequency value, emphasis is placed on the A1 reflected and transmitted values. The A1 and other modes can be identified experimentally by group velocity, as an example, and measurement or adjustment of an angle beam transducer receiving angle. The most interesting results are shown over specific frequency values. Note that there is a monotonic increase in the A1 mode reflection factor amplitude with defect depths around 0.25 MHz and around 0.5 MHz also. In the transmission factor amplitude, there is a monotonic decrease with defect depth around 0.3 MHz.
Fig 2: Lamb wave phase (a) and group (b) velocity dispersion curves for a 10 mm thick Steel plate (c_{L}=5.9 km/sec, c_{T}=3.2 km/sec) |
Fig 3: Variation of reflection (a) and transmission (b) coefficients of the A1 mode for different cases of the ellipse parameter b, that is equal to 10%, 30%, 50% of the wall thickness for an S0 incident mode. (Areas of monotonic behavior of R(A1) and T(A1) are marked with a rectangle.) |
We'll now consider shear horizontal impingement onto the same elliptical defect. Dispersion curves for the steel plate are shown in Figure 4. See [1] for computational details. To illustrate BEM utility for SH wave scattering in a wave guide, a sample problem of n=1 mode impingement onto a series of different depth elliptical defects is illustrated in Figure 5. Note in through transmission the monotonic decrease in amplitude as defect thru wall size increases for almost the entire frequency range 0.25 to 0.8 MHz. Transmitted amplitude as a function of frequency is approximately constant which is also a useful result.
Fig 4: SH phase (a) and group (b) velocity dispersion curves for a 10 mm thick Steel plate (c_{L}=5.9 km/sec, c_{T}=3.2 km/sec) |
Fig 5: Variation of reflection (a) and transmission (b) coefficients of the n=1 mode for different cases of the ellipse parameter b, that is equal to 10%, 30%, 50% of the wall thickness for the n=1 incident mode |
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