Alternate solution for the cylindrical Helmholtz vector equation applied to helical elastic guided waves in pipes

Haraprasad Kannajosyula; Giovanni F. Nino

doi:10.1117/12.2085542

27 March 2015 Alternate solution for the cylindrical Helmholtz vector equation applied to helical elastic guided waves in pipes

Haraprasad Kannajosyula, Giovanni F. Nino

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Proceedings Volume 9436, Smart Sensor Phenomena, Technology, Networks, and Systems Integration 2015; 94360D (2015) https://doi.org/10.1117/12.2085542
Event: SPIE Smart Structures and Materials + Nondestructive Evaluation and Health Monitoring, 2015, San Diego, California, United States

Abstract

Elastic helical guided wave propagation in pipes that has recently gained importance in applications related to tomography and structural health monitoring is analyzed using an alternate formalism. Closed form exponential function based solutions for the Helmholtz vector equation in cylindrical polar coordinates are derived. Relationship of these alternate solutions for the Helmholtz vector equation with the traditional integer order Bessel function based formulation – that has been established for the corresponding solutions of Helmholtz scalar equation in prior literature – is presented. The solutions are single valued at every point in the physical space, and therefore, unlike traditional non-integer order Bessel function based methods, the formulation presented herein preserves the physical uniqueness of the field quantities involved in the wave propagation. The alternate solutions, when applied to the boundary value problem of an isotropic elastic pipe with stress free boundaries, yield a formulation for helical guided wave propagation. A class of helical guided wave modes that have a constant helix angle across the wall thickness of the pipe is predicted. Dispersion characteristics for guided wave propagation such as phase velocity curves; displacement profiles for some points of interest on the phase velocity curves, for select helical angles are presented. The results are compared against traditional notions about helical guided wave propagation.

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Haraprasad Kannajosyula and Giovanni F. Nino "Alternate solution for the cylindrical Helmholtz vector equation applied to helical elastic guided waves in pipes", Proc. SPIE 9436, Smart Sensor Phenomena, Technology, Networks, and Systems Integration 2015, 94360D (27 March 2015); https://doi.org/10.1117/12.2085542

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KEYWORDS

Waveguides

Wave propagation

Bessel functions

Dispersion

Radio propagation

Phase velocity

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