Guided waves energy velocity in absorbing and non-absorbing plates

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 val...

[1]  Deschamps,et al.  Transient Lamb waves: comparison between theory and experiment , 2000, The Journal of the Acoustical Society of America.

[2]  Lowe,et al.  Comparison between the dispersion curves calculated in complex frequency and the minima of the reflection coefficients for an embedded layer , 2000, The Journal of the Acoustical Society of America.

[3]  Peter Cawley,et al.  Lamb waves in highly attenuative plastic plates , 1998 .

[4]  O. Poncelet,et al.  Lamb waves generated by complex harmonic inhomogeneous plane waves , 1997 .

[5]  O. Poncelet,et al.  Energy velocity of complex harmonic plane waves in viscous fluids , 1997 .

[6]  P. Marston,et al.  Traveling‐wave decomposition of surface displacements associated with scattering by a cylindrical shell: Numerical evaluation displaying guided forward and backward wave properties , 1995 .

[7]  M.J.S. Lowe,et al.  Matrix techniques for modeling ultrasonic waves in multilayered media , 1995, IEEE Transactions on Ultrasonics, Ferroelectrics and Frequency Control.

[8]  P. Marston,et al.  Enhancement of the backscattering of high‐frequency tone bursts by thin spherical shells associated with a backwards wave: Observations and ray approximation , 1994 .

[9]  J. Conoir,et al.  Study of Lamb waves based upon the frequency and angular derivatives of the phase of the reflection coefficient , 1993 .

[10]  W. Mayer,et al.  Investigation of Lamb waves having a negative group velocity , 1988 .

[11]  F. Mainardi.  Energy velocity for hyperbolic dispersive waves , 1987 .

[12]  P. Borejko.  INHOMOGENEOUS PLANE WAVES IN A CONSTRAINED ELASTIC BODY , 1987 .

[13]  Herbert Überall,et al.  Resonance theory of acoustic waves interacting with an elastic plate , 1979 .

[14]  M. Hayes,et al.  On energy flux and group velocity , 1979 .

[15]  M. Hayes.  A note on group velocity , 1977, Proceedings of the Royal Society of London. A. Mathematical and Physical Sciences.

[16]  A. Meitzler.  Backward Wavetransmission of Stress Pulses in Elastic Cylinders and Plates , 1963 .

[17]  Maurice A. Biot,et al.  General Theorems on the Equivalence of Group Velocity and Energy Transport , 1957 .

[18]  L. Broer.  On the propagation of energy in linear conservative waves , 1951 .