2012/09/16 by Yang Liu, Ehsan Khajeh, Liu, Yang +5
Engineering · Materials Science · Physics and Astronomy · #Classical Physics (physics.class-ph) #FOS: Physical sciences #Material Properties and Failure Mechanisms #Rock Mechanics and Modeling #Ultrasonics and Acoustic Wave Propagation #physics.class-ph
paper · pdf · doi:10.48550/arxiv.1209.3521
36 pages, 6 figures, to appear in Journal of the Acoustical Society of America
openalex publication_date 2012/09/16 · arxiv created 2012/09/19 · arxiv updated 2012/09/20 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
The nonlinear forcing terms for the wave equation in general curvilinear coordinates are derived based on a hyperelastic material. The expressions for the nonlinear part of the first Piola-Kirchhoff stress are specialized for axisymmetric torsional and longitudinal fundamental wave fields in a cylinder. The matrix characteristics of the nonlinear forcing terms and secondary mode wavestructures are manipulated to analyze the higher harmonic generation due to the guided wave mode self interactions and mutual interactions. It is proven that both torsional and longitudinal mode secondary fields can be cumulative by specific type of guided wave mode interactions. A method for the selection of preferred fundamental excitations that generate strongly cumulative higher harmonics is formulated, and described in detail for second harmonic generation. Hyperelastic finite element models are built to simulate second harmonic generation by T(0,3) and L(0,4) modes. A linear increase of the modal amplitude ratio A2/A12 over the propagation distance is observed for both cases, which indicates mode L(0,5) is effectively generated as cumulative second harmonics.