Wave structure analysis of guided waves in a bar with an arbitrary cross-section

Abstract

Both dispersion curves and wave structures, which are displacement distributions on a bar cross-section, are essential for guided wave NDEs. Theoretical dispersion curves and wave structures for a bar with an arbitrary cross-section are derived in this paper using a special modeling technique called the semi-analytical finite element method (SAFEM). The guidelines for guided wave NDEs of bar-like structures are also shown based on wave structure and modal analysis. First, the relationship between the dispersion curves and their corresponding wave structures were obtained for a square rod. Modes with longitudinal vibration have higher group velocities and torsional modes have constant phase and group velocities. Next, the relationship between the dispersion curves and wave structures for a rail are detailed. The rail is used to represent a bar with a complex cross-section. Similar to the square rod results, the rail's longitudinal modes have higher group velocities. However, the rail contains modes with local vibration. Finally, single mode detection and excitation techniques are introduced. A single mode can be obtained by detecting and exciting with a weighted function that corresponds to a specific mode's wave structure.

Vibration energy analysis of a plate for defect imaging with a scanning laser source technique

“…[27][28][29][30][31][32][33][34] Because this technique requires only division of the cross section of a bar-like structure, guided wave propagation can be carried out more efficiently than in the case of general finite element analysis, which requires a whole region to be divided into small elements. Moreover, the SAFE method is suitable for modal analysis because wave fields in a bar-like structure are expressed as the sum of guided wave modes.…”

“…The semianalytical finite element (SAFE) method, [27][28][29][30][31][32][33][34] an efficient calculation technique for guided waves, was used in the numerical analyses. Propagation energy in a plate is discussed in this paper using the velocity vectors and stress tensors in the SAFE formulation, and elastic wave energy generated in a plate with a crack is discussed using the calculation results.…”

Numerical studies of nonlinear ultrasonic guided waves in uniform waveguides with arbitrary cross sections

“…The SAFE method has been developed to investigate the propagation of guide waves along arbitrary cross-sectional geometries, such as railways, 32,34 square rods, 35 grooved plates…”

Guided wave propagation in metallic and resin plates loaded with water on single surface

“…This is because the generation efficiency of quasi-Scholte waves is strongly dependent on frequency. It is known that applying external loading similar to the wave structure of a certain mode of Lamb wave can generate the mode efficiently [12]. Because the mode shown in Fig.…”