한국음향학회지 (The Journal of the Acoustical Society of Korea)

  • 제33권3호
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  • Pages.191-199
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  • 2014
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  • 1225-4428(pISSN)
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  • 2287-3775(eISSN)
한국음향학회 (The Acoustical Society of Korea)
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국부적 불연속을 갖는 도파관을 따라 전파되는 파동에 대한 파수 영역 유한 요소 해석

Propagation of Structural Waves along Waveguides with Non-Uniformities Using Wavenumber Domain Finite Elements

  • Ryue, Jungsoo (School of Naval Architecture and Ocean Engineering, University of Ulsan)
  • 투고 : 2014.02.07
  • 심사 : 2014.04.15
  • 발행 : 2014.05.31
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⟨ 이전 논문 다음 논문 ⟩

초록

파이프, 평판과 같이 단면의 형상이 길이 방향으로 일정한 도파관 구조물을 따라 전파되는 진동의 반사 및 투과 특성은 여러 공학 분야에서 응용되는 중요한 주제이다. 도파관에 조인트 또는 균열 등의 국부적 불연속이 있는 경우, 스펙트럴 요소(spectral element)와 유한 요소(finite elment)를 결합한 SE/FE 방법이 주로 사용되고 있다. 그러나 이 방법은 보 이론에 기반한 스펙트럴 요소가 사용되므로 저주파수 대역 해석에 국한되는 단점이 있다. 고주파수 대역 해석에는 스펙트럴 수퍼 요소(spectral super element)와 유한 요소를 결합한 SSE/FE 방법이 제안되었으나 유한요소와 스펙트럼 요소의 연성으로 인해 많은 연산 시간이 요구된다. 이러한 문제점을 개선하고자, 본 연구에서는 국부적 불연속 구간의 단면이 일정한 경우에 대해 국부적 불연속 구간을 스펙트럴 수퍼 요소로 대체한 SSE/SSE 연성 해석을 시도하였다. 적용 모델로는 국부적 결함을 가진 레일의 파동 반사 및 투과, 그리고 주기적 보강재를 가진 평판의 진동전파에 대해 적용하였다. 결함을 가진 레일의 해석 예를 통해, 본 논문에서 사용한 SSE/SSE 방법과 기존의 SSE/FE 방법의 성능을 비교하였다. 보강재를 가진 평판의 예를 통해서는 반복 구조를 가진 도파관의 파동 전파 특성 해석에 SSE/SSE 방법이 유용함을 확인하였다.

Wave reflection and transmission characteristics in waveguides are an important issue in many engineering applications. A combined spectral element and finite element (SE/FE) method is used to investigate the effects of local non-uniformities but limited at relatively low frequencies because the SE is formulated by using a beam theory. For higher frequency applications, a method named a combined spectral super element and finite element (SSE/FE) method was presented recently, replacing spectral elements with spectral super elements. This SSE/FE approach requires a long computing time due to the coupling of SSE and FE matrices. If a local non-uniformity has a uniform cross-section along its short length, the FE part could be further replaced by SSE, which improves performance of the combined SSE/FE method in terms of the modeling effort and computing time. In this paper SSEs are combined to investigate the characteristics of waves propagating along waveguides possessing geometric non-uniformities. Two models are regarded: a rail with a local defect and a periodically ribbed plate. In the case of the rail example, firstly, the results predicted by a combined SSE/FE method are compared with those from the combined SSEs in order to justify that the combined SSEs work properly. Then the SSEs are applied to a ribbed plate which has periodically repeated non-uniformities along its length. For the ribbed plate, the propagation characteristics are investigated in terms of the propagation constant.

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참고문헌

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