Investigation of Lamb waves having a negative group velocity
56
Citation
0
Reference
10
Related Paper
Citation Trend
Abstract:
The propagation characteristics of Lamb waves in a solid plate are typically represented by a set of dispersion curves, which describe the Lamb-wave phase velocity as a function of the product fd, where f is the acoustic frequency and d is the plate thickness. For certain modes, within a range of phase velocity and fd, it has been theoretically predicted that the associated group velocity could be negative, i.e., the energy transport is in the opposite direction to the phase velocity. In the present study, Lamb waves are generated via mode conversion from a water-borne sound beam incident onto a flat brass plate. Measurement of the phase and group velocities of the Lamb waves of the S1 mode is performed for the fd range of 2.0–2.3 MHz-mm. Comparison of the measured and computed values of phase and group velocities shows good agreement and clearly demonstrates that S1-mode Lamb waves have a negative group velocity for fd=2.08–2.24 MHz-mm.Keywords:
Group velocity
Lamb waves
Phase velocity
Cite
The simplest dispersion laws for dissipative media, density of electromagnetic energy, phase and group velocities been considered. It has been shown that group velocity may exceed the velocity of light. Also it has been shown that for polar dielectrics with abnormal positive dispersion described by Deby's formula the velocity of energy coincides with phase velocity
Group velocity
Phase velocity
Dispersion relation
Velocity dispersion
Cite
Citations (0)
We considered the negative group velocity of plate-mode waves. Lamb waves are a typical example of existence of negative group velocity. However, if we try to apply the negative group velocity of Lamb waves to some applications such as acoustical flat lenses, there is a problem about the existence of negative group velocity of Lamb waves. Its existence depends only on Poisson's ratio. That is, the negative group velocities of Lamb waves depend only on physical parameters of materials. Consequently, we considered to control a negative group velocity. The negative group velocity of Lamb-type waves in a solid/liquid/solid structure can be controlled by changing the thickness of a liquid layer. In this research, we considered the relationships between the existence of negative group velocities and the parameters of each layer material with respect to Lamb-type waves in a solid/liquid/solid structure by numerical calculation. As a result, it was confirmed that the negative group velocity of Lamb-type waves depended not only on Poisson's ratio but also on the density of each layer and the longitudinal wave velocity of the liquid layer. This result is useful when the negative group velocity of Lamb-type waves is applied to acoustical flat lenses, which require the negative group velocity.
Lamb waves
Group velocity
Phase velocity
Poisson's ratio
Cite
Citations (17)
An elastic wave with negative group velocity transports wave energy in the direction opposite to the phase velocity. This phenomenon has been predicted in certain modes of Lamb waves. This is still difficult to believe, despite the fact that some experimental evidence has been reported so far. In this paper, direct evidence of the negative group velocity is presented which was obtained by means of visualization of pulsed Lamb waves propagating on a glass plate in A2 mode.
Lamb waves
Group velocity
Phase velocity
Cite
Citations (19)
We derive both 3-D and 2-D Fréchet sensitivity kernels for surface-wave group-delay and anelastic attenuation measurements. A finite-frequency group-delay exhibits 2-D off-ray sensitivity either to the local phase-velocity perturbation δc/c or to its dispersion ω(∂/∂ω)(δc/c) as well as to the local group-velocity perturbation δC/C. This dual dependence makes the ray-theoretical inversion of measured group delays for 2-D maps of δC/C a dubious procedure, unless the lateral variations in group velocity are extremely smooth.
Group velocity
Phase velocity
Velocity dispersion
Cite
Citations (22)
A Lamb wave guided by a plate structure has dispersive characteristics because phase and group velocity change with the variation of frequency and thickness. The Lamb wave has two modes, symmetric and anti-symmetric mode, which propagates symmetrically and non-symmetrically with respect to centerline. In this paper, the derivation of Lamb wave equation with anisotropic material property is investigated. The phase velocity and group velocity dispersion curves are shown using the stiffness matrix of composite materials with the variation of angle.
Lamb waves
Phase velocity
Group velocity
Dispersion relation
Matrix (chemical analysis)
Cite
Citations (0)
It is proved by theory and experiment that the arrival time of elastic scattering wave is determined by group velocity of Lamb wave in plate and the speed of elastic scattering wave in water. The frequency dispersion equation of Lamb wave is derived for submerged elastic plate, and the phase velocity and group velocity dispersion curves are obtained by numerical calculation method. It is found that the phase velocity is greater or less than the group velocity at different frequency-thickness products. The energy propagation speed of wave is group velocity, so the arrival time of elastic scattering wave is determined by group velocity of Lamb wave in plate and the speed of sound in water. Experimental results show that elastic scattering wave is ahead of or behind the edge wave in echoes of elastic steel plate. The experiment results confirm validity of the theoretical analysis results.
Lamb waves
Group velocity
Phase velocity
Wave shoaling
Dispersion relation
Cite
Citations (0)
The phase velocity and group velocity dispersion curves of composite material plate are calculated and plotted by using dichotomy method in MATLAB.The actuating frequency,pulse and actuating shape are designed by dispersion curve of Lamb wave.The dynamic response signals of the composite plate are obtained by finite element method.Damage location is calculated by the actual group velocity of Lamb wave and time of flight of the difference signal before and after damage.
Lamb waves
Group velocity
Phase velocity
Composite plate
SIGNAL (programming language)
Cite
Citations (1)
The motivation of this work is to study the group velocity of Lamb waves in anisotropic plates in order to understand the characteristics of the propagation of wave packets in arbitrary directions. The group velocity equations have been derived, taking into account the spatial dispersion (variation of the velocity with the direction of propagation) as well as the frequency dispersion. For bulk waves, it is already well known that anisotropy implies a difference between group velocity and phase velocity. It is shown here that this phenomenon occurs for Lamb waves as well, affecting both the velocity and the direction of propagation. An experimental demonstration is also given, using a plate composed of a unidirectional Glass Epoxy composite. The obtained experimental curves are in good agreement with the theoretical calculations.
Group velocity
Phase velocity
Lamb waves
Dispersion relation
Love wave
Cite
Citations (22)
The propagation characteristics of Lamb waves in a solid plate are typically represented by a set of dispersion curves, which describe the Lamb-wave phase velocity as a function of the product fd, where f is the acoustic frequency and d is the plate thickness. For certain modes, within a range of phase velocity and fd, it has been theoretically predicted that the associated group velocity could be negative, i.e., the energy transport is in the opposite direction to the phase velocity. In the present study, Lamb waves are generated via mode conversion from a water-borne sound beam incident onto a flat brass plate. Measurement of the phase and group velocities of the Lamb waves of the S1 mode is performed for the fd range of 2.0–2.3 MHz-mm. Comparison of the measured and computed values of phase and group velocities shows good agreement and clearly demonstrates that S1-mode Lamb waves have a negative group velocity for fd=2.08–2.24 MHz-mm.
Group velocity
Lamb waves
Phase velocity
Cite
Citations (56)
A disposable digital microfluidic system is realized using sensor plate/thin water layer/piezoelectric substrate. It is important to clarify the Lamb wave mode, which propagates in the sensor plate. In this paper, the phase velocity of the Lamb wave was experimentally estimated and compared with the Rayleigh-Lamb equation. Also, the acoustic streaming velocity was experimentally obtained. The results indicate that the high phase velocity is realized by decreasing plate thickness and increasing the operating frequency.
Lamb waves
Phase velocity
Rayleigh Wave
Mode (computer interface)
Cite
Citations (0)