2000 Fiscal Year Final Research Report Summary
Development of a Practical Method of Simulating Three-Dimensional Acoustic Fields in Closed Space with Arbitrary Shape Using Analytic Solutions
| Project/Area Number |
11650255
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Dynamics/Control
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| Research Institution | Shizuoka Institute of Science and Technology |
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Principal Investigator |
URATA Yoshihiko Shizuoka Institute of Science and Technology, Faculty of Science and Technology, Professor, 理工学部, 教授 (60024329)
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| Project Period (FY) |
1999 – 2000
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| Keywords | Helmholtz Equation / Eigevalue / Analytic Solution / Arbitrarily shaped domain / Collocation method / Accuracy / Experiment / 高精度 |
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| Research Abstract |
The purpose of this research is to develop a method of calculating approximately eigenvalue problems of Helmholtzs Equation governing steady acoustic fields. In this method, analytic solutions represented in three-dimensional polar coordinates are used. The solutions consist of the spherical Bessel functions in the radial direction, the Legendre associated functions in the zenith angle direction and the trigonometric functions in the azimuth angle direction. The collocation method is utilized to satisfy approximately boundary conditions. This method can be applied to problems of axisymmetric spatial domains.
As examples of the cases in which the exact solutions can be obtained, eigenvalues of a rectangular parallelepiped and a circular cylinder are calculated by this method. The results agree with the exact values. Furthermore, calculations about a boxy domain with round edges and a frustum of pyramid are done. An experiment is done about the frustum of pyramid. The calculated natural frequencies and the natural modes agree well with the experimental results.
We can conclude that the present method is valid. To expand application of the method, however, more investigations are necessary.
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