Three-Dimensional Investigation of the Propagation of Waves in Hollow Circular Cylinders. I. Analytical Foundation

Abstract

The propagation of free harmonic waves along a hollow circular cylinder of infinite extent is discussed within the framework of the linear theory of elasticity. A characteristic equation appropriate to the circular hollow cylinder is obtained by use of the Helmholtz potentials for arbitrary values of the physical parameters involved. Axially symmetric waves, the limiting modes of infinite wavelength, and a special family of equivoluminal modes are derived and discussed as degenerate cases of the general equations.

Structural Health Monitoring of Steel Pipes under Different Boundary Conditions and Choice of Signal Processing Techniques

“…For the gouged pipe, peaks which are weaker than the defectfree pipe are selected at 620 and 1220 kHz. The possible propagating modes can be F (1,2) or F (1,3). For the dented pipe, the major peaks occur at 500 and 1180 kHz which corresponds to F(1, 2) and/or F(1, 3) mode.…”

“…In summary, it can be stated that when water flows through the pipes strong F(1, 2) and F(1, 3) modes propagate through the wall of the defect-free pipe at slightly higher frequency (>1000 kHz). For the gouged pipe, the possible propagating modes are weak F(1, 2) and F (1,3). For the dented pipe, the possible propagating modes are F(1, 2) and F (1, 3).…”

“…In order to identify the propagating guided wave modes through the defective and defect-free pipes, phase velocities are calculated from the peaks in the experimental V ( f ) curves using Snell's law , or all of them together. For the defect-free pipe, the strongest peak occurs at 1140 kHz which means that the strongest propagating modes could be F(1, 2), L(0, 2) or F (1,3). For the gouged pipe, the peaks could be selected at 580, 700, and 1180 kHz (Figure 2(a)), and the corresponding guided wave modes can be identified as F (1,2), L(0, 2), and F(1, 3) (Figure 2(b)).…”

“…For the defect-free pipe, the strongest peak occurs at 1140 kHz which means that the strongest propagating modes could be F(1, 2), L(0, 2) or F (1,3). For the gouged pipe, the peaks could be selected at 580, 700, and 1180 kHz (Figure 2(a)), and the corresponding guided wave modes can be identified as F (1,2), L(0, 2), and F(1, 3) (Figure 2(b)). The strong peak at 700 kHz for the gouged pipe corresponds to the F(1, 2) propagating mode.…”

“…Gazis [1,2] first analytically solved the propagation of harmonic waves in an infinitely long elastic hollow cylinder. Many investigators [3,4] used guided wave modes for detecting wall thinning defects in cylindrical pipes.…”