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Modeling and Computation for Dynamics of Rotating Flexible Structure
Posted On Thursday, November 13, 2008 at at 10:25 PM by Yongan HuangThis is very important research topics, especiall in space engineering. In these engineering simulation, it usually is long time to get the simulation results. However, the computational errors are obvious effect on the simulation results. So the simplectic algorithm, which is a geometric algorith, is adopted to compute these model. The precise integration method(On precise integration method) is also used to eliminate the errors of the computers.
Usually, DAEs (Differential Algebraic Equation) is the mathematical model of multibody dynamics. It is very difficult to solve this kind of equations by conventional algorithm.
This paper presents an improved symplectic precise integration method (PIM) to increase the accuracy and keep the stability of the computation of the rotating rigid–flexible coupled system. Firstly, the generalized Hamilton's principle is used to establish a coupled model for the rotating system, which is discretized and transferred into Hamiltonian systems subsequently. Secondly, a suitable symplectic geometric algorithm is proposed to keep the computational stability of the rotating rigid–flexible coupled system. Thirdly, the idea of PIM is introduced into the symplectic geometric algorithm to establish a symplectic PIM, which combines the advantages of the accuracy of the PIM and the stability of the symplectic geometric algorithm. In some sense, the results obtained by this method are analytical solutions in computer for a long span of time, so the time-step can be enlarged to speed up the computation. Finally, three numerical examples show the stability of computation, the accuracy of solving stiff equations and the capability of solving nonlinear equations, respectively. All these examples prove the symplectic PIM is a promising method for the rotating rigid–flexible coupled systems.
Journal of Sound and Vibration, Volume 299, Issues 1-2, 9 January 2007, Pages 229-246, doi:10.1016/j.jsv.2006.07.009
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Paper Two: Modeling and Computation for Dynamics of Flexible Structure
This paper is presented to improve the modeling accuracy and the computational stability for a high-speed rotating flexible structure. The differential governing equations are derived based on the first-order approximation coupling (FOAC) model theory in the framework of the generalized Hamiltonian principle. The semi-discrete model is obtained by the finite element method, and a new shape function based on FOAC is established for the piezoelectric layers. To increase the efficiency, accuracy, and stability of computation, first, the second-order half-implicit symplectic Runge–Kutta method is presented to keep the computational stability of the numerical simulation in a long period of time. Then, the idea of a precise integration method is introduced into the symplectic geometric algorithm. An improved symplectic precise integration method is developed to increase accuracy and efficiency. Several numerical examples are adopted to show the promise of the modeling and the computational method.
J. Vib. Acoust. / Volume 130 / Issue 4 / August 2008 -- 041005 (15 pages) http://dx.doi.org/10.1115/1.2890386
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