Abstract:The influence of material attenuation on Lamb wave dispersion behavior has been studied analytically. As the attenuation is increased, keeping the ratio of the bulk longitudinal to bulk shear wave attenuation constant at the value measured in high-density polyethylene, the degree of coupling between the shear and longitudinal partial waves decreases and the phase velocity dispersion curves for different modes of the same symmetry can cross; this is not possible for an elastic plate. With increasing attenuation… Show more
“…For a pipe of inner radius 1 a and outer radius 1 b , and uniform defect of outer radius 2 a , the plane wave reflection coefficient pw Λ is given as The mode matching predictions shown in Fig. 3 were obtained using only 6 quadratic finite elements, which is sufficient to deliver convergence to two decimal places for the reflection coefficient at a frequency of 150 kHz.…”
Section: Uncoated Pipementioning
confidence: 99%
“…Barshinger and Rose [2] extended the work to the analysis of a number of viscoelastic layers and published dispersion curves for a steel pipe coated with epoxy. Both Chan and Cawley [1] and Barshinger and Rose [2] use analytic techniques to derive the governing dispersion relation, and Barshinger and Rose later discuss the problems this presents when it comes to finding the roots of this equation. Here, the addition of a viscoelastic layer means that the roots of the dispersion relation are complex and it is much harder to locate these roots in the complex plane (see also Simonetti and Cawley [3] for a discussion on coated plates).…”
Section: Introductionmentioning
confidence: 99%
“…For example, Chan and Cawley [1] studied the effect of viscoelasticity on the dispersion curves for a high density polyethylene pipe. Energy dissipation was included by adding an imaginary component to the Lamé constants, although modal attenuation was studied only for Lamb modes in a plate.…”
Long range ultrasonic testing is now a well established method for examining in-service degradation in pipelines. In order to protect pipelines from the surrounding environment it is common for viscoelastic coatings to be applied to the outer surface. These coatings are, however, known to impact on the ability of long range ultrasonic techniques to locate degradation, or defects, within a coated pipe. The coating dissipates sound energy travelling along the pipe, attenuating both the incident and reflected signals making responses from defects difficult to detect. This article aims to investigate the influence of a viscoelastic coating on the ability of long range ultrasonic testing to detect a defect in an axisymmetric pipe. The article focuses on understanding the behaviour of the fundamental torsional mode and quantifying the effect of bitumen coatings on reflection coefficients generated by axisymmetric defects. Reflection coefficients are measured experimentally for coated and uncoated pipes and compared to theoretical predictions generated using numerical mode matching and a hybrid finite element technique. Good agreement between prediction and measurement is observed for uncoated pipes, and it is shown that the theoretical methods presented here are fast and efficient making them suitable for studying long pipe runs. However, when studying coated pipes agreement between theory and prediction is observed to be poor for predictions based on those bulk acoustic properties currently reported in the literature for bitumen. Good agreement is observed only after conducting a parametric study to identify more appropriate values for the bulk acoustic properties. Furthermore, the reflection coefficients obtained for the fundamental torsional mode in a coated pipe show that significant sound attenuation is present over relatively short lengths of coating, thus quantifying those problems commonly encountered with the use of long range ultrasonic testing on coated pipes in the field.3
“…For a pipe of inner radius 1 a and outer radius 1 b , and uniform defect of outer radius 2 a , the plane wave reflection coefficient pw Λ is given as The mode matching predictions shown in Fig. 3 were obtained using only 6 quadratic finite elements, which is sufficient to deliver convergence to two decimal places for the reflection coefficient at a frequency of 150 kHz.…”
Section: Uncoated Pipementioning
confidence: 99%
“…Barshinger and Rose [2] extended the work to the analysis of a number of viscoelastic layers and published dispersion curves for a steel pipe coated with epoxy. Both Chan and Cawley [1] and Barshinger and Rose [2] use analytic techniques to derive the governing dispersion relation, and Barshinger and Rose later discuss the problems this presents when it comes to finding the roots of this equation. Here, the addition of a viscoelastic layer means that the roots of the dispersion relation are complex and it is much harder to locate these roots in the complex plane (see also Simonetti and Cawley [3] for a discussion on coated plates).…”
Section: Introductionmentioning
confidence: 99%
“…For example, Chan and Cawley [1] studied the effect of viscoelasticity on the dispersion curves for a high density polyethylene pipe. Energy dissipation was included by adding an imaginary component to the Lamé constants, although modal attenuation was studied only for Lamb modes in a plate.…”
Long range ultrasonic testing is now a well established method for examining in-service degradation in pipelines. In order to protect pipelines from the surrounding environment it is common for viscoelastic coatings to be applied to the outer surface. These coatings are, however, known to impact on the ability of long range ultrasonic techniques to locate degradation, or defects, within a coated pipe. The coating dissipates sound energy travelling along the pipe, attenuating both the incident and reflected signals making responses from defects difficult to detect. This article aims to investigate the influence of a viscoelastic coating on the ability of long range ultrasonic testing to detect a defect in an axisymmetric pipe. The article focuses on understanding the behaviour of the fundamental torsional mode and quantifying the effect of bitumen coatings on reflection coefficients generated by axisymmetric defects. Reflection coefficients are measured experimentally for coated and uncoated pipes and compared to theoretical predictions generated using numerical mode matching and a hybrid finite element technique. Good agreement between prediction and measurement is observed for uncoated pipes, and it is shown that the theoretical methods presented here are fast and efficient making them suitable for studying long pipe runs. However, when studying coated pipes agreement between theory and prediction is observed to be poor for predictions based on those bulk acoustic properties currently reported in the literature for bitumen. Good agreement is observed only after conducting a parametric study to identify more appropriate values for the bulk acoustic properties. Furthermore, the reflection coefficients obtained for the fundamental torsional mode in a coated pipe show that significant sound attenuation is present over relatively short lengths of coating, thus quantifying those problems commonly encountered with the use of long range ultrasonic testing on coated pipes in the field.3
“…Additionally, Lamb waves can have relatively low attenuation over long distances relative to bulk waves [9,10]. However, GW methods must contend with the dispersive and multi-modal nature of GW.…”
“…Deschmps et al [17] have studied acoustic emission and reflection in an anisotropic plate. 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.…”
This paper reports on a study of the propagation characteristics of visco-elastic, Rayleigh-like waves in stratified half-space structures. Beginning with the Kelvin model, the characterization equation and the normal displacement of visco-elastic Rayleigh waves in stratified half-space structures are derived and the influence of the visco-elastic modulus on dispersion and attenuation is discussed. Theoretical calculations show that the attenuation-frequency curves perfectly match the phase-frequency curves. The effect of visco-elasticity on the attenuation of the Rayleigh-like wave is larger than its effect on dispersion. For "weak viscosity," the attenuation is directly proportional to the viscosity modulus and the shear viscosity has a greater impact on the dispersion curves than does the bulk viscosity. The transient response of a visco-elastic Rayleigh wave is also simulated by means of Laplace and Hankel inversion transforms. The results are in good agreement with the theoretic predictions. It is believed the paper's results and conclusions will provide insights and guidance for estimating visco-elastic parameters and for assessing adhesive quality.
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