The Journal of the Acoustical Society of Korea (한국음향학회지)

The Acoustical Society of Korea (한국음향학회)
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A Numerical Method for Wave Reflection and Transmission Due to Local Non-Uniformities in Waveguides at High Frequencies

국부적 불연속을 가진 도파관의 고주파수 대역 파동 반사 및 투과 해석 기법

  • 유정수 (울산대학교 조선해양공학부)
  • Received : 2010.04.01
  • Accepted : 2010.05.27
  • Published : 2010.07.31
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Abstract

In waveguide structures, waves may be partially reflected by local non-uniformities. The effects of local non-uniformities has been previously investigated by means of a combined spectral element and finite element (SE/FE) method at relatively low frequencies. However, since the SE is formulated based on a beam theory, the SE/FE method is not appropriated for analysis at higher frequencies where complex deformation of the waveguide occurs. So it is necessary to extend this approach for high frequencies. For the wave propagation at higher frequencies, a combined spectral super element and finite element (SSE/FE) method is introduced in this paper. As an example of the application of this method, wave reflection and transmission due to a local defect in a rail are simulated at frequencies between 20kHz and 30kHz. Also numerical errors are evaluated by means of the conservation of the incident power.

도파관 (waveguide structures)에 지지구조 또는 균열과 같은 국부적 불연속이 존재하는 경우, 도파관을 따라 전파되는 파동은 이러한 국부적 불연속으로 인해 반사가 발생한다. 빔과 같이 단면의 형상이 단순한 도파관에서는 국부적 불연속에 의한 저주파수 대역 반사 및 투과 특성을 스펙트럴요소(spectral element, SE)와 유한요소(finite element, FE)를 연결한 스펙트럴요소/유한요소법 (SE/FE method)으로 해석 할 수 있다. 그러나 도파관의 단면 형상이 복잡하거나 또는 고주파수 대역 해석에서는 빔 이론에 근거한 스펙트럴 요소를 이용하는 것이 부적합하다. 본 논문에서는 고주파수 대역 파동 반사 및 투과 특성 해석을 위해 스펙트럴요소 대신 스펙트럴수퍼요소 (spectral super element, SSE)를 도입하고, 이를 유한요소와 결합시킨 SSE/FE 방법을 제안한다. 이 방법은 도파관 모델링에 스펙트럴 수퍼요소를 이용하므로 레일과 같이 단면의 형상이 복잡한 도파관의 고주파수 대역 해석에 적합하다. 본 논문에서는 SSE/FE 해석에 필요한 반무한 SSE(semi-infinite spectral super element)에 대한 정식화를 먼저 수행하고, 이를 FE로 모델링한 국부적 불연속 구간과 연결하여 SSE/FE 모델을 구성하였다. 이 방법의 적용 예로써 단순 형상의 국부적 결함이 존재하는 철로 레일에 대하여 고주파수 대역 파동반사 및 투과계수를 계산하고 그 결과를 살펴보았다. 또한, 입사된 파워가 보존되어야 한다는 조건을 이용해 SSE/FE 방법의 수치오차를 추정하였다.

Keywords

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