Numerical simulation of ultrasonic guided waves using the Scaled Boundary Finite Element Method

Abstract

The formulation of the Scaled Boundary Finite Element Method is applied for the computation of dispersion properties of ultrasonic guided waves. The cross-section of the waveguide is discretized in the Finite Element sense, while the direction of propagation is described analytically. A standard eigenvalue problem is derived to compute the wave numbers of propagating modes. This paper focuses on cylindrical waveguides, where only a straight line has to be discretized. Higher-order elements are utilized for the discretization. As examples, dispersion curves are computed for a homogeneous pipe and a layered cylinder.

Computation of dispersion curves for embedded waveguides using a dashpot boundary condition

“…In previous work, 9,32,43 detailed formulations have been presented to compute dispersion properties of guided waves in plates, axisymmetric structures, and general threedimensional waveguides, respectively. For all geometries, the waveguide's cross-section is discretized in the finite element sense, while the direction of wave propagation is described analytically.…”

Laplace Domain Boundary Element Method for Structural Health Monitoring of Poly-Crystalline Materials at Micro-Scale

“…These methods include the Finite Element Method (FEM) [16,17], Finite Difference Method (FDM) [18][19][20], Finite Volume Method (FVM) (also known as Finite Integration Technique (FIT) [21]), and Boundary Element Method (BEM) [9,22]. Studies have shown that ultrasonic scattering or attenuation can be used to characterize poly-crystalline micro-structures and to localize flaws [17,23,24]. Establishing the relationship between ultrasonic scattering/attenuation and material parameters enables reliable and high-quality material testing [25,26].…”

“…Specifically, the experimental ToA value was measured at 13.10 [µs], while the corresponding numerical value was recorded as 13. 23 [µs], thus resulting in a small relative error of 0.983%. The observed consistency between the experimental and numerical results indicated a reliable correspondence between the physical measurements and the numerical modeling.…”

“…Figures [21][22][23] present illustrative examples for each effect, thus visually demonstrating the configurations of the cracks within the micro-structure.…”

“…The comparison revealed a strong agreement between the two sets of results in terms of ToA, amplitude, and wave velocity. Specifically, the experimental ToA value was measured at 13.10 [µs], while the corresponding numerical value was recorded as 13 23. [µs], thus resulting in a small relative error of 0.983%.…”