능동 동조질량감쇠의 고층빌딩 해석을 위한 동적압축법
A Dynamic Condensation for Tall Buildings with Active Tuned Mass Damper
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초록
자유도 수가 많은 고층 구조물의 해석하기 위해 모든 층에 sensors를 설치하는 것은 비 실용적이다. 따라서 이러한 문제를 해결하기 위해 "reduced-order control" 방법이 소개되었다. 본 논문은 동적압축법(dynamic condensation method)이 제안되었다. 이 압축법은 반복법으로 "Guyan condensation"의 initial approximation을 적용하였다. 본 논문에서 제시된 동적압축법(dynamic condensation)은 원하는 값을 얻을 때까지 지속적으로 updated가 되며, 결과는 기존의 "Guyan condensation"보다 정확한 결과를 나타내었다. 또한 "eigenvalue shifting technique"을 적용하여 iteration으로 계산되는 시간을 크게 단축하였다. "Reduced-order system"을 도입하기 위한 두가지 schemes이 토의되었다. 제시된 동적압축법 효과의 증명을 위해 능동 동조질량감쇠 고층빌딩의 수치 해석이 토의되었고, 단지 두 번의 반복(iterations)을 통한 결과는 매우 정확한 것으로 나타났다.
Abstract
It is impractical to install sensors on every floor of a tall building to measure the full state vector because of the large number of degrees of freedom. This makes it necessary to introduce reducedorder control. A kind of system reduction scheme (dynamic condensation method) is proposed in this paper. This method is iterative and Guyan condensation is looked upon as an initial approximation of the iteration. Since the reducedorder system is updated repeatedly until a desired one is obtained, the accuracy of the reducedorder system resulting from the proposed method is much higher than that obtained from the Guyan condensation method. An eigenvalue shifting technique is applied to accelerate the convergence of iteration. Two schemes to establish the reducedorder system by using the proposed method are also presented and discussed in this paper. The results for a tall building with active tuned mass damper show that the proposed method is efficient for the reducedorder modelling and the accuracy is very close to exact only after two iterations.
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