title: Analysis of second harmonic guided waves in pipes using a large-radius asymptotic approximation for axis-symmetric longitudinal modes.
abstract: 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.
authors: Department of Engineering Science and Mechanics, The Pennsylvania State University, 16802 PA, USA. vkc5017@psu.edu
authors: Vamshi Krishna
authors: VK
authors: Chillara
authors: Cliff J
authors: CJ
authors: Lissenden