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Research Papers

Modeling and Computation for the High-Speed Rotating Flexible Structure

[+] Author and Article Information
Yong-an Huang1

State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, P.R.C.; School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R.C.yahuang@hust.edu.cn

Zhou-ping Yin, You-lun Xiong

State Key Laboratory of Digital Manufacturing Equipment and Technology, Huazhong University of Science and Technology, Wuhan 430074, P.R.C.; School of Mechanical Science and Engineering, Huazhong University of Science and Technology, Wuhan 430074, P.R.C.

1

Corresponding author.

J. Vib. Acoust 130(4), 041005 (Jul 01, 2008) (15 pages) doi:10.1115/1.2890386 History: Received September 21, 2007; Revised November 14, 2007; Published July 01, 2008

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.

Copyright © 2008 by American Society of Mechanical Engineers
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Figures

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Figure 1

The RFS with a hub, a section-variational beam, and a tip mass

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Figure 2

Parameters of the beam

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Figure 3

Deformations of the beam

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Figure 4

The finite element model of the beam

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Figure 5

The tip transverse displacement of the flexible beams of the four kinds of structures

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Figure 6

The axial extension of the flexible beams of the four kinds of structures

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Figure 7

The slope displacement of the flexible beams of the four kinds of structures

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Figure 8

Configuration of a RFS with piezoelectric layers

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Figure 9

(a) Time history of tip transverse deflections of Structures A, B, and C. (b) Time history of tip transverse deflections Structures A, B, and C.

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Figure 10

(a) Time history of tip axial extensions of Structures A, B, and C. (b) Time history of tip axial extensions fo structures A, B, and C.

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Figure 11

(a) Time history of tip transverse deflections of Structures B and D. (b) Time histroy of tip transverse deflections of Structures B and D.

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Figure 12

(a) Transverse displacements of Structures D and E. (b) Transverse displacements of Structures D and E.

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Figure 13

The symplectic Runge–Kutta method and the general Runge–Kutta algorithm with a step size of 0.0001

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Figure 14

The result simulated by the symplectic Runge–Kutta method with a step size of 0.0001

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Figure 15

The result simulated by the Runge–Kutta method with a step size of 0.0001

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Figure 16

The total energy computed by the symplectic Runge–Kutta method with a step size of 0.0001

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Figure 17

The total energy computed by the Runge–Kutta method with a step size of 0.0001

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Figure 18

The total energy computed by the symplectic Runge–Kutta method with a step size of 0.0005

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Figure 19

The total energy computed wrongly by the Runge–Kutta method with a step size of 0.0005

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Figure 20

Results of state x1 calculated by the symplectic precise integration method, precise integration method, Runge–Kutta method, and analytical solution with a step size of 0.05

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Figure 21

The error between the analytical solution and symplectic precise integration method with a step size of 0.05

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Figure 22

Results of state x1 calculated by the symplectic precise integration method, precise integration method, Runge–Kutta method, and analytical solution with a step size of 0.01

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Figure 23

The error between the analytical solution and symplectic precise integration method with a step size of 0.01

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Figure 24

The error between the analytical solution and precise integration method with a step size of 0.01

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Figure 25

The error between the analytical solution and Runge–Kutta method with a step size of 0.01

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Figure 26

Structure of compound pendulum

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Figure 27

State x calculated by the Runge–Kutta method with a step size of 0.0001 and by the symplectic precise integration method with a step size of 0.01

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Figure 28

State β calculated by the Runge–Kutta method with a step size 0.0001 and by the symplectic precise integration method with a step size of 0.01

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