Analysis of second harmonic guided waves in pipes using a large-radius asymptotic approximation for axis-symmetric longitudinal modes

Theoretical formulation for the problem of second harmonic guided waves in pipes is presented from the principles of continuum mechanics. The formulation is carried out in the reference configuration of the pipe with an emphasis on the correct use of the “Divergence” operator in the reference configuration. Second harmonic guided wave generation from axis-symmetric longitudinal guided wave modes is studied. A large radius asymptotic approximation for the wave structures in pipe is studied and an error estimate for the same is obtained. Comparison with the corresponding modes in a plate and the analogy to second harmonic guided wave generation in plates is presented.

► We studied the second harmonic guided waves in pipes using an asymptotic solution.
► We compared the wave structures with the corresponding modes in the plate.
► Only asymptotic symmetric modes can be efficiently generated as second harmonics.