Guided waves energy velocity in absorbing and non-absorbing plates

Abstract

This paper presents a study of the velocity of the propagation of energy in guided waves in plates. The motivation of the work comes from the practical observation that the conventional approach to predicting the velocities of pulses or wave packets, that is, the simple group velocity calculation, breaks down when the guided waves are attenuative. The conventional approach is therefore not valid for guided waves in absorbing materials or for leaky waves. The paper presents a theoretical derivation of an expression to predict the energy velocity of guided waves in an isotropic plate, based on the integration of the Poynting energy vectors. When applied to modes with no attenuation, it is shown analytically from this expression that the energy velocity is always identical to the group velocity. On the other hand, when applied to attenuative modes, numerical integration of the expression to yield the true energy velocity shows that this can differ quite significantly from the group velocity. Experimental validation of the expression is achieved by measuring the velocity of wave packets in an absorbing plate, under such conditions when the energy velocity differs substantially from the group velocity. Excellent agreement is found between the predictions and the measurements. The paper also shows the Poynting vectors in the various model studies, and some interesting phenomena relating to their directions.

Interaction of lamb modes with delaminations in plates coated by highly absorbing materials

“…Acoustic waves (in particular shear waves) in such polymers are strongly absorbed. The propagation length of shear waves can be as short as only a few wavelengths, rendering the accurate determination of shear wave velocity and attenuation a complicated problem [13]- [19]. However, high absorption in the coating layer has a considerable influence on the structure of Lamb modes, and on their interaction with defects.…”

Structural Diagnostics of CFRP Composite Aircraft Components by Ultrasonic Guided Waves and Built-In Piezoelectric Transducers

“…Since the waves are attenuated, the propagation speed does not coincide with the classical group velocity, c gr =∂ω/∂k [163]. In this case the wavenumber is complex.…”

Propagation characteristic of laser-generated visco-elastic Rayleigh-like waves in stratified half-space

“…Considering the epoxy coatings as a visco-elastic solid, regarding the volumetric deformation as approximately elastic, and the shear deformation is visco-elastic, by using the Kelvin mode and Eq. (19), the phase velocityfrequency curves for K η = 0, K η = 0.1ηs and K η = 1ηs are plotted in Fig. 6.…”

“…Chan and Cawley [18] have discussed the effect on Lame waves brought about by viscosity through changing imaginary part of phase velocity. Bernard and Lowe [19] have studied the velocity of energy propagation in a visco-elastic plate. However, in order to simplify the calculation, most of the researches adopt Kelvin-Voigt model which directly append an imaginary part (damping) to the phase velocity and the frequency dispersion caused by visco-elasticity is ignored.…”