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Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain


Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email:

Describing an Axisymmetric Notch in a Pipe Using Singularities

Journal of Applied Nonlinear Dynamics 1(4) (2012) 321--339 | DOI:10.5890/JAND.2012.09.003

D.K. Stoyko$^{1}$,$^{3}$, N. Popplewell$^{1}$, A.H. Shah$^{2}$

$^{1}$ Department of Mechanical and Manufacturing Engineering, University of Manitoba, 15 Gillson Street, Winnipeg, Manitoba, Canada, R3T 5V6

$^{2}$ Department of Civil Engineering, University of Manitoba, 15 Gillson Street,Winnipeg, Manitoba, Canada, R3T 5V6

$^{3}$ Stress Engineering Services Canada, #125, 12111 - 40th Street S.E., Calgary, Alberta, Canada, T2Z 4E6

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A hybrid Semi-Analytical Finite Element (SAFE) and standard finite element procedure is adopted to ultrasonically but locally detect and characterize an axisymmetric open notch in an infinitely long steel pipe. Interactions between incident, dispersive guided waves and the notch are shown numerically to change a radial displacement’s temporal history and introduce additional singularities in the previously unblemished pipe’s Frequency Response Function (FRF). Differences between the frequencies of the singularities of the unblemished and notched pipes appear to reflect the notch’s dimensions. They also indicate the location of a nearby notch.


All three authors acknowledge the financial support from the Natural Science and Engineering Research Council (NSERC) of Canada. The first author also wishes to acknowledge financial aid from the Society of Automotive Engineers (SAE) International, University ofManitoba, Province ofManitoba, Ms.A. Toporeck and family, and the University of Manitoba Students’ Union (UMSU).


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