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Weakly nonlinear waves generated by vibration of a spherical body
| Title: | Weakly nonlinear waves generated by vibration of a spherical body |
| Authors: | Yano, Takeru Browse this author | | Inoue, Yoshinori Browse this author |
| Issue Date: | Jan-1992 |
| Publisher: | American Institute of Physics (The Acoustical Society of America) |
| Journal Title: | The Journal of the Acoustical Society of America |
| Volume: | 91 |
| Issue: | 1 |
| Start Page: | 69 |
| End Page: | 78 |
| Publisher DOI: | 10.1121/1.402621 |
| Abstract: | The nonlinear propagation of directional spherical waves generated in an unbounded inviscid ideal gas by vibratory motions with small but finite amplitude and moderate frequency of a spherical body is considered. Starting with a regular perturbation expansion for a velocity potential in the near field, a higher-order problem is investigated in the far field up to the shock formation distance. It is thereby shown that, in the far field concerned, a well-known simple far-field equation remains valid for the radial velocity u* including higher-order corrections up to O(εN/r) (N<–1/ε lnε ), where r is a nondimensional radial coordinate and ε(≪1) is the expansion parameter of the expansion. A boundary condition appropriate to the equation, which ensures the matching of a far-field solution with a near-field solution, can be determined from the near-field solution obtained by the regular perturbation procedure. As an application of the theory, the third-order problem is solved for weakly nonlinear acoustic waves radiated by a pulsating sphere. It is further shown that, for weakly nonlinear cylindrical waves with moderate frequency, a similar far-field equation becomes invalid at the third approximation in the far field up to the shock formation distance. |
| Rights: | Copyright 1992, Acoustical Society of America. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the Acoustical Society of America. |
| Type: | article |
| URI: | http://hdl.handle.net/2115/14919 |
| Appears in Collections: | 工学院・工学研究院 (Graduate School of Engineering / Faculty of Engineering) > 雑誌発表論文等 (Peer-reviewed Journal Articles, etc)
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Submitter: 矢野 猛
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