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Development of a Practical Method of Simulating Three-Dimensional Acoustic Fields in Closed Space with Arbitrary Shape Using Analytic Solutions

Research Project

Project/Area Number 11650255
Research Category

Grant-in-Aid for Scientific Research (C)

Allocation TypeSingle-year Grants
Section一般
Research Field Dynamics/Control
Research InstitutionShizuoka Institute of Science and Technology

Principal Investigator

URATA Yoshihiko  Shizuoka Institute of Science and Technology, Faculty of Science and Technology, Professor, 理工学部, 教授 (60024329)

Project Period (FY) 1999 – 2000
Project Status Completed (Fiscal Year 2000)
Budget Amount *help
¥200,000 (Direct Cost: ¥200,000)
Fiscal Year 2000: ¥200,000 (Direct Cost: ¥200,000)
KeywordsHelmholtz Equation / Eigevalue / Analytic Solution / Arbitrarily shaped domain / Collocation method / Accuracy / Experiment / 高精度 / 閉空間 / 音場 / 解析解 / 任意形状 / 精度 / 三次元 / 極座標 / 節点配置 / 能率
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.

Report

(3 results)
  • 2000 Annual Research Report   Final Research Report Summary
  • 1999 Annual Research Report
  • Research Products

    (3 results)

All Other

All Publications (3 results)

  • [Publications] 浦田喜彦,内野光一郎: "解析解による三次元ヘルムホルツ方程式系の解析"日本機械学会論文集(C編). 67. 1322-1329 (2001)

    • Description
      「研究成果報告書概要(和文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] Y.URATA and K.UCHINO: "Analysis of Three-Dimensional Problems Described by Helmboltz Equation Using Analytic Solutions (A Basic Study on the Collocation method)"Trans.JSME (C). Vol.67, No.657. 1322-1329 (2001)

    • Description
      「研究成果報告書概要(欧文)」より
    • Related Report
      2000 Final Research Report Summary
  • [Publications] 浦田喜彦,内野光一郎: "解析解による三次元ヘルムホルツ方程式系の解析"日本機械学論文集C編. (掲載決定).

    • Related Report
      2000 Annual Research Report

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Published: 2000-04-01   Modified: 2016-04-21  

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