# Analytic Solution to the Spatial Propagation of the Flexible Structures

• 발행 : 2001.12.01
• 34 3

#### 초록

In this paper, a singularity problem of the state transition matrix is investigated in the spatial propagation when the spatial matrix differential equation is constructed via time finite element analysis. A parametric study shows that the degree of singularity of the state transition matrix depends on the degree of flexibility of the structures. As an alternative to avoid the numerical problems due to the singularity, an analytic solution fur spatial propagation of the flexible structures is proposed. In the proposed method, the spatial properties of the structure are analytically expressed by a combination of transcendental functions. The analytic solution serves fast and accurate results by eliminating the possibility of the error accumulation caused by the boundary condition. Several numerical examples are shown to validate the effectiveness of the proposed methods.

#### 키워드

상태천이행렬;특이성;공간전파;시간 유한요소해석;해석적 해

#### 참고문헌

1. Kwakernaak, H. and Sivan, R, 1972, Linear Optimal Control System, John Wiley & Sons, USA
2. Borri, M., Ghiringhelli, G., Lanz, M., Mantegazza, P., and T. Merlini, 1985, 'Dynamic Response of Mechanical Systems by a Weak Hamiltonian Formulation,' Computer and Structures Vol. 20, No. 1-3, pp. 495-508 https://doi.org/10.1016/0045-7949(85)90098-7
3. 장인식, 맹주원, 1999, '시간유한요소법에서 선형형상함수를 이용한 자동 시간간격제어 기법,' 대한기계학회논문집(A), 제23권, 제2호, pp. 190-198
4. Suk, J. and Kim, Y., 1998, 'Time Domain Finite Element Analysis of Dynamic Systems,' AIAA Journal, Vol. 36, No. 7, pp. 1312-1319
5. 박정훈, 유홍희, 1998, '끝단질량 및 관성모멘트를 갖는 회전외팔보의 면외방향 진동해석,' 대한기계학회논문집(A), 제22권, 제7호, pp. 1299-1306
6. Bailey, C., 1975, 'Application of Hamiltons Law of Varying Action,' AIAA Journal, vol. 13, 1154-1157
7. Simkins, T., 1978, 'Unconstrained Variational Statements for Initial and Boundary Value Problems,' AIAA Journal Vol. 16, pp. 559-563
8. Turner, J. and Chun, H., 1984, 'Optimal Distributed Control of a Flexible Spacecraft During A Large-Angle Maneuver,' Journal of Guidance Control and Dynamics, Vol. 7, No. 3, pp.257-264
9. Kane, T., Ryan, R., and Banerjee, A., 1987, 'Dynamics of a Cantilever Beam attached to a Moving Base,' Journal of Guidance, Control and Dynamics, Vol. 10, No. 2, pp. 139-151
10. Heyden, T., 2000, 'They are Flying High,' Newsweek, Vol. 454
11. Meirovitch, L. and Baruh, H., 1982, 'Control of Self-Adjoint Distributed Parameter Systems,' Journal of Guidance, Control and Dynamics, Vol. 5, No. 1, pp. 60-66