This paper describes a ray superposition theory for cumulative growth of nonlinear effects in a two‐dimensional acoustic mode, based on decomposition of the mode into a pair of obliquely propagating, nonlinear planar waves. The mathematical foundation of the formulation is an earlier perturbation analysis of the reflection of a distorted planar wave obliquely incident on the boundary of an infinite half‐space [Z. Qian, Sci. Sin. 25, 492–501 (1982)]. Based on the results of the analysis, each of the pair of rays forming the signal at a selected field point is traced back to its origin at the excitation. Each ray is described as a simple planar wave undergoing finite amplitude distortion that depends on the propagation distance along that ray between field and source points. This distance is the same for each ray at a specified field point, but differences in the excitation at the respective source points result in phase differences between the two rays. The overall signal is shown to be the same as a modal description of the propagation [H. C. Miao and J. H. Ginsberg, J. Acoust. Soc. Am. 80, 911–920 (1986)]. The ray solution explains an apparent paradox in the modal analysis, which indicated that although the signal can be resolved into a pair of planar waves, the distortion process is scaled only by the axial position along the waveguide. Conversely, the earlier solution provides validation for the superposition of rays, as well as for the linear reflection law. [Work supported by NSF and ONR.]
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May 1988
August 13 2005
Ray solution for finite amplitude two‐dimensional waves in a hard‐walled rectangular waveguide
Kun‐tien Shu;
Kun‐tien Shu
School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332
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J. H. Ginsberg
J. H. Ginsberg
School of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332
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J. Acoust. Soc. Am. 83, S4 (1988)
Citation
Kun‐tien Shu, J. H. Ginsberg; Ray solution for finite amplitude two‐dimensional waves in a hard‐walled rectangular waveguide. J. Acoust. Soc. Am. 1 May 1988; 83 (S1): S4. https://doi.org/10.1121/1.2025381
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