Reflection and Transmission Coefficients from Rectangular Notches in Pipes

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STOYKO, Darryl Keith;POPPLEWELL, Neil ;SHAH, Arvind H..
Reflection and Transmission Coefficients from Rectangular Notches in Pipes. 
Strojniški vestnik - Journal of Mechanical Engineering, [S.l.], v. 60, n.5, p. 349-362, june 2018. 
ISSN 0039-2480.
Available at: <https://www.sv-jme.eu/article/reflection-and-transmission-coefficients-from-rectangular-notches-in-pipes/>. Date accessed: 16 apr. 2021. 
doi:http://dx.doi.org/10.5545/sv-jme.2014.1836.
Stoyko, D., Popplewell, N., & Shah, A.
(2014).
Reflection and Transmission Coefficients from Rectangular Notches in Pipes.
Strojniški vestnik - Journal of Mechanical Engineering, 60(5), 349-362.
doi:http://dx.doi.org/10.5545/sv-jme.2014.1836
@article{sv-jmesv-jme.2014.1836,
	author = {Darryl Keith Stoyko and Neil  Popplewell and Arvind H. Shah},
	title = {Reflection and Transmission Coefficients from Rectangular Notches in Pipes},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {60},
	number = {5},
	year = {2014},
	keywords = {Pipe, Notch, Cutoff Frequency, Singularity, Guided Waves},
	abstract = {The use of a single, non-dispersive ultrasonic guided wave mode is one important approach to monitoring a structure’s health. It is advantageously non-destructive with the ability of propagating over tens of metres to detect a hidden defect. The dimensional assessment of a defect, on the other hand, requires reflection coefficients for two or more such modes. Multiple modes may be excited simultaneously by applying a short pulse to a structure’s external surface. This situation is examined here for a circular, hollow and homogeneous, isotropic pipe having negligible damping and an open rectangular notch. A finite element model is employed in a region around a notch. It is coupled to a wave function expansion in the two adjacent, effectively, semi-infinite pipes. Representative longitudinal and flexural modes are investigated for different notch dimensions. A nonaxisymmetric notch, unlike an axisymmetric notch, introduces a plethora of cross modal couplings that lead to more singularities in a reflection coefficient’s frequency dependence. There is, however, a common pattern to these distinctive singularities. It is conjectured that singularities corresponding to propagating modes may enable a notch to be detected and its dimensions determined.},
	issn = {0039-2480},	pages = {349-362},	doi = {10.5545/sv-jme.2014.1836},
	url = {https://www.sv-jme.eu/article/reflection-and-transmission-coefficients-from-rectangular-notches-in-pipes/}
}
Stoyko, D.,Popplewell, N.,Shah, A.
2014 June 60. Reflection and Transmission Coefficients from Rectangular Notches in Pipes. Strojniški vestnik - Journal of Mechanical Engineering. [Online] 60:5
%A Stoyko, Darryl Keith
%A Popplewell, Neil 
%A Shah, Arvind H.
%D 2014
%T Reflection and Transmission Coefficients from Rectangular Notches in Pipes
%B 2014
%9 Pipe, Notch, Cutoff Frequency, Singularity, Guided Waves
%! Reflection and Transmission Coefficients from Rectangular Notches in Pipes
%K Pipe, Notch, Cutoff Frequency, Singularity, Guided Waves
%X The use of a single, non-dispersive ultrasonic guided wave mode is one important approach to monitoring a structure’s health. It is advantageously non-destructive with the ability of propagating over tens of metres to detect a hidden defect. The dimensional assessment of a defect, on the other hand, requires reflection coefficients for two or more such modes. Multiple modes may be excited simultaneously by applying a short pulse to a structure’s external surface. This situation is examined here for a circular, hollow and homogeneous, isotropic pipe having negligible damping and an open rectangular notch. A finite element model is employed in a region around a notch. It is coupled to a wave function expansion in the two adjacent, effectively, semi-infinite pipes. Representative longitudinal and flexural modes are investigated for different notch dimensions. A nonaxisymmetric notch, unlike an axisymmetric notch, introduces a plethora of cross modal couplings that lead to more singularities in a reflection coefficient’s frequency dependence. There is, however, a common pattern to these distinctive singularities. It is conjectured that singularities corresponding to propagating modes may enable a notch to be detected and its dimensions determined.
%U https://www.sv-jme.eu/article/reflection-and-transmission-coefficients-from-rectangular-notches-in-pipes/
%0 Journal Article
%R 10.5545/sv-jme.2014.1836
%& 349
%P 14
%J Strojniški vestnik - Journal of Mechanical Engineering
%V 60
%N 5
%@ 0039-2480
%8 2018-06-28
%7 2018-06-28
Stoyko, Darryl, Neil  Popplewell, & Arvind H. Shah.
"Reflection and Transmission Coefficients from Rectangular Notches in Pipes." Strojniški vestnik - Journal of Mechanical Engineering [Online], 60.5 (2014): 349-362. Web.  16 Apr. 2021
TY  - JOUR
AU  - Stoyko, Darryl Keith
AU  - Popplewell, Neil 
AU  - Shah, Arvind H.
PY  - 2014
TI  - Reflection and Transmission Coefficients from Rectangular Notches in Pipes
JF  - Strojniški vestnik - Journal of Mechanical Engineering
DO  - 10.5545/sv-jme.2014.1836
KW  - Pipe, Notch, Cutoff Frequency, Singularity, Guided Waves
N2  - The use of a single, non-dispersive ultrasonic guided wave mode is one important approach to monitoring a structure’s health. It is advantageously non-destructive with the ability of propagating over tens of metres to detect a hidden defect. The dimensional assessment of a defect, on the other hand, requires reflection coefficients for two or more such modes. Multiple modes may be excited simultaneously by applying a short pulse to a structure’s external surface. This situation is examined here for a circular, hollow and homogeneous, isotropic pipe having negligible damping and an open rectangular notch. A finite element model is employed in a region around a notch. It is coupled to a wave function expansion in the two adjacent, effectively, semi-infinite pipes. Representative longitudinal and flexural modes are investigated for different notch dimensions. A nonaxisymmetric notch, unlike an axisymmetric notch, introduces a plethora of cross modal couplings that lead to more singularities in a reflection coefficient’s frequency dependence. There is, however, a common pattern to these distinctive singularities. It is conjectured that singularities corresponding to propagating modes may enable a notch to be detected and its dimensions determined.
UR  - https://www.sv-jme.eu/article/reflection-and-transmission-coefficients-from-rectangular-notches-in-pipes/
@article{{sv-jme}{sv-jme.2014.1836},
	author = {Stoyko, D., Popplewell, N., Shah, A.},
	title = {Reflection and Transmission Coefficients from Rectangular Notches in Pipes},
	journal = {Strojniški vestnik - Journal of Mechanical Engineering},
	volume = {60},
	number = {5},
	year = {2014},
	doi = {10.5545/sv-jme.2014.1836},
	url = {https://www.sv-jme.eu/article/reflection-and-transmission-coefficients-from-rectangular-notches-in-pipes/}
}
TY  - JOUR
AU  - Stoyko, Darryl Keith
AU  - Popplewell, Neil 
AU  - Shah, Arvind H.
PY  - 2018/06/28
TI  - Reflection and Transmission Coefficients from Rectangular Notches in Pipes
JF  - Strojniški vestnik - Journal of Mechanical Engineering; Vol 60, No 5 (2014): Strojniški vestnik - Journal of Mechanical Engineering
DO  - 10.5545/sv-jme.2014.1836
KW  - Pipe, Notch, Cutoff Frequency, Singularity, Guided Waves
N2  - The use of a single, non-dispersive ultrasonic guided wave mode is one important approach to monitoring a structure’s health. It is advantageously non-destructive with the ability of propagating over tens of metres to detect a hidden defect. The dimensional assessment of a defect, on the other hand, requires reflection coefficients for two or more such modes. Multiple modes may be excited simultaneously by applying a short pulse to a structure’s external surface. This situation is examined here for a circular, hollow and homogeneous, isotropic pipe having negligible damping and an open rectangular notch. A finite element model is employed in a region around a notch. It is coupled to a wave function expansion in the two adjacent, effectively, semi-infinite pipes. Representative longitudinal and flexural modes are investigated for different notch dimensions. A nonaxisymmetric notch, unlike an axisymmetric notch, introduces a plethora of cross modal couplings that lead to more singularities in a reflection coefficient’s frequency dependence. There is, however, a common pattern to these distinctive singularities. It is conjectured that singularities corresponding to propagating modes may enable a notch to be detected and its dimensions determined.
UR  - https://www.sv-jme.eu/article/reflection-and-transmission-coefficients-from-rectangular-notches-in-pipes/
Stoyko, Darryl, Popplewell, Neil, AND Shah, Arvind.
"Reflection and Transmission Coefficients from Rectangular Notches in Pipes" Strojniški vestnik - Journal of Mechanical Engineering [Online], Volume 60 Number 5 (28 June 2018)

Authors

Affiliations

  • Stress Engineering Services Canada, Alberta, T2Z 4E6, Canada 1
  • University of Manitoba, Department of Mechanical and Manufacturing Engineering, Canada 2
  • University of Manitoba, Department of Civil Engineering, Canada 3

Paper's information

Strojniški vestnik - Journal of Mechanical Engineering 60(2014)5, 349-362

https://doi.org/10.5545/sv-jme.2014.1836

The use of a single, non-dispersive ultrasonic guided wave mode is one important approach to monitoring a structure’s health. It is advantageously non-destructive with the ability of propagating over tens of metres to detect a hidden defect. The dimensional assessment of a defect, on the other hand, requires reflection coefficients for two or more such modes. Multiple modes may be excited simultaneously by applying a short pulse to a structure’s external surface. This situation is examined here for a circular, hollow and homogeneous, isotropic pipe having negligible damping and an open rectangular notch. A finite element model is employed in a region around a notch. It is coupled to a wave function expansion in the two adjacent, effectively, semi-infinite pipes. Representative longitudinal and flexural modes are investigated for different notch dimensions. A nonaxisymmetric notch, unlike an axisymmetric notch, introduces a plethora of cross modal couplings that lead to more singularities in a reflection coefficient’s frequency dependence. There is, however, a common pattern to these distinctive singularities. It is conjectured that singularities corresponding to propagating modes may enable a notch to be detected and its dimensions determined.

Pipe, Notch, Cutoff Frequency, Singularity, Guided Waves