Transactions of the Korean Society of Mechanical Engineers A (대한기계학회논문집A)

The Korean Society of Mechanical Engineers (대한기계학회)
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Optimal Shape Design of Pyeongyeong Considering Structural and Acoustical Characteristics

구조-음향 특성을 고려한 편경의 최적 형상 설계

  • Received : 2013.12.05
  • Accepted : 2013.12.31
  • Published : 2014.03.01
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Abstract

An optimal shape design algorithm is suggested to systematically design a traditional Korean musical instrument, the Pyeongyeong. The Pyeongyeong consists of 16 different chime stones called Gyeongpyeons. The first natural vibration frequency of each Gyeongpyeon must be adjusted to its target frequency, which is determined by the traditional sound tuning method. The second and third natural frequencies must be proportional to the first natural frequency with a specific ratio (1:1.498:2.378). The key idea in our suggested design algorithm is to use the sensitivity of natural frequencies to the variation in the length of each side of a Gyeongpyeon. The dimensions of five different Gyeongpyeons are determined by following the suggested algorithm. Changes in natural frequencies with respect to local thickness variation are closely investigated to compensate for errors that may occur during manufacturing.

한국 전통 악기인 편경을 체계적으로 설계하기 위한 최적 형상 설계 알고리즘을 제안한다. 편경은 16 개의 서로 다른 크기의 경편으로 구성되어 있다. 각 경편의 첫 번째 진동 고유 주파수는 전통 소리 튜닝 방법에 의해 결정되는 특정 주파수에 일치하여야 하고, 두 번째와 세 번째 진동 고유 주파수들은 첫 번째 진동 고유 주파수와 단 3 화음 관계(1:1.498:2.378)를 가져야 한다. 제안한 설계 알고리즘의 핵심은 경편의 각 변의 길이 변화에 따른 고유 주파수의 민감도를 구하고, 이를 이용하여 위 두 가지 설계 목적에 부합하는 경편의 치수를 결정하는 것이다. 제안하는 방법으로 5 개의 서로 다른 경편의 형상 치수를 결정하였다. 그리고, 제작 과정에서 발생할 수 있는 오차를 보상하기 위해, 경편의 국부적인 두께 변화에 따른 진동 고유 주파수의 변화에 대해서도 살펴보았다.

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References

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