Wave mode extraction from multimodal wave signals in an orthotropic composite plate.

In this paper the post-processing procedure based on the mode orthogonality is applied to extract individual waveforms at a composite plate edge from multimodal signals. To obtain the amplitudes of individual modes, numerically predicted modal through-thickness stress and displacement field values are used in the orthogonality relation. The performance of the mode extraction technique is evaluated by processing signals obtained from Finite Element (FE) modeling and experimental measurements. The propagation of the overlapping wave packets of Lamb modes S0 and A0 is considered along the fiber direction and perpendicular to that direction. The required experimental two-dimensional displacement components at the plate edge are measured by 3D Scanning Laser Doppler Vibrometer (3D SLDV). It is demonstrated that S0 mode can be extracted very well from the signal but A0 mode with slightly poorer accordance with the original waveforms and numerical predictions.

Application of orthogonality-relation for the separation of Lamb modes at a plate edge: numerical and experimental predictions.

In this study the orthogonality relation-based method for post-processing finite element (FE) predictions and experimental measurements is applied in order to separate Lamb modes at a plate edge at normal incidence. The scattered wave field from the free edge is assumed to be a superposition of all the eigenmodes of an infinite plate. The eigenmode amplitudes of the reflected wave field are determined by implementing the orthogonality-based method on the measured plate edge displacements. Overlapping wavepackets of Lamb modes at a plate edge are simulated by using the FE model and the experiment in the case of an incident S0 mode in a plate with a notch. In the experiment a 3D Scanning Laser Doppler Vibrometer (3D SLDV) (Johansmann and Sauer, 2005) is used to measure 3 dimensional vibrations and thus the edge two-dimensional displacement components simultaneously. It is demonstrated that it is possible to extract signals of various propagating and non-propagating modes in time-domain. The influences of the errors in practical measurements on the extraction procedure have also been studied.

Scattering of the fundamental torsional mode at an axial crack in a pipe.

A quantitative study of the interaction of the T(0,1) torsional mode with an axial defect in a pipe is presented. The results are obtained from finite element simulations and experiments. The influence of the crack axial extent, depth, excitation frequency, and pipe circumference on the scattering is examined. It is found that the reflection from a defect consists of a series of the wave pulses with gradually decaying amplitudes. Such behavior is caused by the shear waves diffracting from the crack and then repeatedly interacting with the crack due to circumferential propagation. Time-domain reflection coefficient analysis demonstrates that the trend of the reflection strength for different crack lengths, pipe diameters, and frequencies from a through-thickness crack satisfies a simple normalization. The results show that the reflection coefficient initially increases with the crack length at all frequencies but finally reaches an oscillating regime. Also, at a given frequency and crack length the reflection decreases with the increase in pipe circumference. An additional scattering study of the shear wave SH(0) mode at a part-thickness notch in a plate shows that the reflection coefficient, when plotted against depth of the notch, increases with both frequency and notch depth.

Scattering of the fundamental shear horizontal mode in a plate when incident at a through crack aligned in the propagation direction of the mode.

A study of the scattering of the fundamental guided wave SH(0) at a through-thickness narrow notch directed along the wave's propagation in a plate is presented. The results are obtained from Finite Element simulations and experimental measurements. Good agreement is found between the simulations and the measurements. The results are shown for a range of crack lengths and shapes. The scattered wave field consists of the reflected and diffracted SH(0) mode and also contributions from mode conversions to the S(0) mode. It is found that the coefficient of direct reflection of the SH(0) mode has an undulating nature depending on the length of the crack. This is caused by interference phenomena that are related to the interaction of different surface wave types generated on the crack surfaces and their diffractions at both tips of the crack. It is shown that the dominating part of this reflection is generated by the delayed "Rayleigh type" surface waves reflected from the far tip of the crack.

Edge resonance in semi-infinite thick pipe: numerical predictions and measurements.

This paper presents theoretical and experimental studies of axisymmetric longitudinal guided wave L(0,2) interaction with the free edge of the pipe. A numerical method based on normal mode superposition is applied to predict the edge resonance by an analysis of dispersion relations of separate modes. In parallel, the finite element analysis and experimental measurements prove the existence of edge resonance in the pipe in case of L(0,2) wave incidence. It is shown that the edge resonance is mainly caused by the first pair of complex modes. Additionally the behavior of edge resonance phenomenon as a function of the curvature of the pipe is studied. The displacement amplitudes measured at the edge demonstrate that the edge resonance is affected by the frequency and thickness to midradius ratio of the pipe, and it is losing its strength in thicker pipes, as the growing difference between the outer and inner radii destroys symmetry. The reflected energy amplitudes show that at the resonance frequencies the incident wave is strongly converted to L(0,1) and L(0,3) modes, depending also on the curvature parameter of the pipe.