Low-frequency reflection characteristics of the s0 Lamb wave from a rectangular notch in a plate

Abstract

An analysis of the reflection of the fundamental Lamb mode s0 from surface-breaking rectangular notches in isotropic plates is presented. The results are obtained from finite element time domain simulations together with experimental measurements. Very good agreement is found between the simulations and the measurements. Results are shown for a range of notch widths and depths, including the special case of a crack, defined as a zero-width notch. An interference phenomenon is identified which explains the periodic nature of the reflection coefficient when plotted as a function of notch width. Finally, an analysis using the S-parameter approach and both low and high frequency asymptotic analyses yields physical explanations of the nature of the reflection behavior from the cracks. It is found that the low frequency (quasistatic) approximation may be used accurately for cracks up to about a quarter of the plate thickness, provided that the quasistatic crack-opening function is chosen such that bending of the plate is omitted. At higher frequencies and depths the functions tend towards the high frequency (ray theory) predictions but these are never accurate models within the nondispersive frequency range of the s0 mode.

Generación de ondas de Lamb en estructuras tipo placa mediante cerámicas piezoeléctricas

“…The branches corresponding to each Lamb mode are clearly identifiable. The Rayleigh-Lamb frequency equations can be written as [1] where +1 applies for symmetric modes, while -1 applies It is well known that Lamb wave modes are sensitive to different types of damage (7,8,9). Whereas the S0 mode is characterized by its dominant stress and displacement components in the direction of propagation, the A0 mode has significant shear stress and lateral displacement components.…”

Photoconductors for Measuring Speckle Motion to Monitor Ultrasonic Vibrations

“…This would include parts inspections for internal cracks and discontinuities (Lowe, 2002). The reason for this is that the S 0 mode suffers very little dispersion, limiting pulse breakup and allowing for better event timing.…”

“…19. Although edge-excitation has been investigated with traditional contact transducers (Lowe, 2002), this novel arrangement is the first all-optical, end-on excitation technique specifically designed to excite only the symmetric mode. With further improvements, it could be adapted to generate in-plane vibrations for testing in any kind of plate-like structure.…”

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“…1. An ultrasonic pulse with a frequency of 100kHz was applied to the top of the bar as pressure following a sinusoidal function as presented by Yagawa and Okuda [4], although in this case two periods of the sine function were used [6,7]. The maximum amplitude of the pulse was 10MPa.…”

“…Defects were modelled as voids, with height 1mm and width 1mm to 7mm. The maximum element size was chosen as 1mm, to exceed the lower threshold suggested by Lowe and Diligent [7] of at least eight elements per wavelength. The timesteps in the simulations were taken as 0.1μs.…”