• Journal of the Korean Society for Nondestructive Testing
• /
• v.30 no.3
• /
• pp.194-199
• /
• 2010

Based on the idea of eigen-mode expansion, a method to analyze the reflection of Lamb wave from a finite vertical discontinuity of plate is theoretically derived and verified by experiment. The theoretical prediction is in good agreement with the experimental result, and this strongly suggests that eigen-mode expansion method could be used for solution of inverse scattering problem for ultrasonic testing using Lamb wave.

• Journal of the Computational Structural Engineering Institute of Korea
• /
• v.31 no.3
• /
• pp.127-132
• /
• 2018

In this paper, a scheme for the evaluation of variability in the eigen-modes of functionally graded material(FGM) beams is proposed within the framework of perturbation-based stochastic analysis. As a random parameter, the spatially varying elastic modulus of FGM along the axial direction at the mid-surface of the beam is chosen, and the thru-thickness variation of the elastic modulus is assumed to follow the original form of exponential variation. In deriving the formulation, the first order Taylor expansion on the eigen-modes is employed. As an example, a simply supported FGM beam having symmetric elastic modulus with respect to the mid-surface is chosen. Monte Carlo analysis is also performed to check if the proposed scheme gives reasonable outcomes. From the analyses it is found that the two schemes give almost identical results of the mean and standard deviation of eigen-modes. With the propose scheme, the standard deviation shape of respective eigen-modes can be evaluated easily. The deviated mode shape is found to have one more zero-slope points than the mother modes shapes, irrespective of order of modes. The amount of deviation from the mean is found to have larger values for the higher modes than the lower modes.

• Journal of Korean Society of Coastal and Ocean Engineers
• /
• v.4 no.1
• /
• pp.1-9
• /
• 1992

Eigen Function Expansion Method(EFEM) and Plane Wave Approximation are employed to study the propagation of linear water waves over trenches. The properties of trapped waves due to depth and ambient current discontinuities and the effect of evanescent modes on wave propagations are investigated. Special attention is paid to the trapped waves, and not only 3-D plots but also B-D plots of wave propagation are presented.