Erratum to “Anomalous Dispersion of the Lamb Mode” (original) (raw)
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Canadian Journal of Physics, 2019
This paper studies the propagation of symmetric and antisymmetric Lamb waves along a 1 mm thick iodic acid plate (HIO3) in the 1–50 MHz frequency range. The Lamb mode propagation along three crystallographic planes was theoretically investigated, for two mutually orthogonal propagation directions. Several frequencies were found that correspond to Lamb modes with zero group velocity (ZGV) and non-null phase velocity values. The first symmetric Lamb mode, S1, was found to possess only one ZGV point, regardless of the propagation direction; higher order symmetric and antisymmetric modes with up to four ZGV points were found, depending on the propagation plane. The dependence of the ZGV frequencies on each elastic constant (c11, c13, c33, c55) of the HIO3 plate material was also investigated by changing the constant values by 5% and 10%. It was found that c33 and c55 affect the number of the ZGV points, while c11 and c13 affect the frequency of the ZGV points. The existence and frequenc...
Influence of the anisotropy on zero-group velocity Lamb modes
The Journal of the Acoustical Society of America, 2009
Guided waves in a free isotropic plate (symmetric S(n) and antisymmetric A(n) Lamb modes) exhibit a resonant behavior at frequencies where their group velocity vanishes while their phase velocity remains finite. Previous studies of this phenomenon were limited to isotropic materials. In this paper, the optical generation and detection of these zero-group velocity (ZGV) Lamb modes in an anisotropic plate is investigated. With a circular laser source, multiple local resonances were observed on a silicon wafer. Experiments performed with a line source demonstrated that the frequency and the amplitude of these resonances depend on the line orientation. A comparison between experimental and theoretical dispersion curves for waves propagating along the [100] and [110] directions of the silicon crystal verified that these resonances occur at the minimum frequency of the S(1) and A(2) Lamb modes. Simulations indicated that it is possible to deduce the three elastic constants of the plate material with good accuracy from these measurements.
Anomalous and negative reflection of Lamb waves in mode conversion
Physical Review B, 2012
Mode conversion is an important feature of wave propagation used in ultrasonic nondestructive testing with Lamb waves. When a wave packet with a given central frequency, and a correspondent central wavenumber, impinges on the free edge of a plate, the reflected wave generally is a weighed combination of all the possible modes compatible with the given frequency. Under particular conditions, only one wave packet is reflected with a distinct central wavenumber compared to the incident one. In such a case, according to Snell's law, the reflection angle is different from the incident one (anomalous reflection). In this article, experimental results are presented on anomalous reflection on a free edge of a thin plate of a Lamb wave packet; moreover, experimental results are reported on a Lamb wave packet that is reflected at an angle lying on the same side, with respect to the normal direction, of the impinging wave (negative reflection). Negative reflection of Lamb waves has been obtained through mode conversion taking place at the free edge of a thin plate of constant thickness: More precisely, a symmetric S1 Lamb mode has been converted into the same mode but with phase velocity antiparallel to group velocity, so obtaining the so-called backward-propagating Lamb wave packet.
Study of the fundamental Lamb modes interaction with asymmetrical discontinuities
NDT & E International, 2008
The interaction of the fundamental Lamb modes with asymmetrical discontinuities in isotropic plates is studied numerically and experimentally. Three kinds of discontinuities that enable mode conversions are considered: steps down, steps up and asymmetrical notches. The anti-symmetrical and symmetrical Lamb modes contributions are separated by means of the simple arithmetic operations of addition and subtraction. The power reflection and transmission
The Journal of the Acoustical Society of America, 2003
Reflection of Lamb waves when the fundamental mode A 0 is incident at the free end of a plate is studied, in order to identify the extent to which the generation of nonpropagating modes influences the field local to the end of the plate. Semi-analytical predictions, finite element simulations, and experimental measurements are presented for frequencies below the A 2 cutoff. First it is shown, for frequencies below the A 1 cutoff, that reflection of the A 0 mode is accompanied by a delay in phase, and that there is significant additional motion due to nonpropagating modes within about five plate thicknesses of the end. The extend of this additional motion in the vicinity of the end of the plate is demonstrated by subtracting the contribution of the propagating modes from the displacement field. The wave field at frequencies above the A 1 cutoff is more complex because the A 1 as well as the A 0 propagating modes are present at the end of the plate. Nevertheless, it has still been possible, using semi-analytical predictions and finite element simulations, to demonstrate the additional motion due to the nonpropagating modes.
Lamb Modes for an Isotropic Incompressible Plate
Mathematical Problems in Engineering, 2013
Lamb modes for an incompressible isotropic plate behave in a manner different from those for a compressible plate. The plateau region disappears and anomalous behavior of modes does not exist.
The nonlinear S0 Lamb mode in a plate with a linearly-varying thickness
Ultrasonics, 2018
The aim of this paper is to investigate propagation characteristics and the generation mechanism of the nonlinear lowest-order symmetric Lamb mode (S 0) which propagates downslope in free elastic plates with slowly linearly varying-thickness. From theoretical analyses, in a low frequency-thickness product (fd) range, the S 0 mode is slightly dispersive, it is easy to generate, and it approximately satisfies the principle of the phase velocity matching. Therefore, if a S 0 mode is excited at a proper frequency in the low fd range, the amplitude of the second harmonic wave is linearly increasing in a certain propagating-distance, which is valuable for the practical NDE application of the second harmonic wave. Moreover, numerical simulations and experiments have been carried out to validate theoretical results. Our investigation of properties of the second harmonic wave can be applied to characterize and evaluate micro-structural damages in varying-thickness waveguides.
Higher-Order Mode Conversion of Symmetric and Antisymmetric Lamb Waves in Periodic Plates
In this paper, we consider the codirectional mode coupling of the higher-order Lamb wave modes S 2 and A 2 in an infinite elastic plate with sinusoidal surface corrugation. The multiple-scales perturbation technique is used to derive coupled-mode equations describing the amplitudes of interacting modes. The analysis is carried out for the general case when the wavenumbers k s2 of the symmetric mode and k A2 of the antisymmetric mode satisfy the resonance condition: k A2 − k s2 = kw. The coupled amplitude equations are solved exactly. It is shown that the modes periodically exchange their energies as they propagate along the plate with complete conversion from one mode into the other when the resonance condition is exactly satisfied. The effect of detuning away from resonance also shows periodic exchange but without complete conversion with the energy balance in favor of the excited mode.