Modeling and Computation for the High-Speed Rotating Flexible Structure

2008 ◽  
Vol 130 (4) ◽  
Author(s):  
Yong-an Huang ◽  
Zhou-ping Yin ◽  
You-lun Xiong
Keyword(s):  
High Speed ◽  
Integration Method ◽  
Order Approximation ◽  
Computational Method ◽  
Flexible Structure ◽  
Computational Stability ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Piezoelectric Layers ◽  
First Order Approximation

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.

scholarly journals Precise Integration Method for Solving Noncooperative LQ Differential Game

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Hai-Jun Peng ◽  
Sheng Zhang ◽  
Zhi-Gang Wu ◽  
Biao-Song Chen
Keyword(s):  
Differential Equation ◽  
Differential Game ◽  
Integration Method ◽  
Transformation Method ◽  
Linear Quadratic ◽  
Riccati Differential Equation ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Direct Integration Method ◽  
Two Parameters

The key of solving the noncooperative linear quadratic (LQ) differential game is to solve the coupled matrix Riccati differential equation. The precise integration method based on the adaptive choosing of the two parameters is expanded from the traditional symmetric Riccati differential equation to the coupled asymmetric Riccati differential equation in this paper. The proposed expanded precise integration method can overcome the difficulty of the singularity point and the ill-conditioned matrix in the solving of coupled asymmetric Riccati differential equation. The numerical examples show that the expanded precise integration method gives more stable and accurate numerical results than the “direct integration method” and the “linear transformation method”.

Extension of the Wittrick-Williams Algorithm to Mixed Variable Systems

1997 ◽  
Vol 119 (3) ◽  
pp. 334-340 ◽  
Author(s):  
Zhong Wanxie ◽  
F. W. Williams ◽  
P. N. Bennett
Keyword(s):  
Timoshenko Beam ◽  
Stiffness Matrix ◽  
Integration Method ◽  
Dynamic Stiffness ◽  
Integration Algorithm ◽  
Precise Integration ◽  
Matrix Computations ◽  
Precise Integration Method ◽  
Count Method ◽  
Mixed Variable

A precise integration algorithm has recently been proposed by Zhong (1994) for dynamic stiffness matrix computations, but he did not give a corresponding eigenvalue count method. The Wittrick-Williams algorithm gives an eigenvalue count method for pure displacement formulations, but the precise integration method uses a mixed variable formulation. Therefore the Wittrick-Williams method is extended in this paper to give the eigenvalue count needed by the precise integration method and by other methods involving mixed variable formulations. A simple Timoshenko beam example is included.

A Strictly Defined Orthogonal Global Task Coordinate Frame and its Contouring Control Application on Biaxial Systems

2019 ◽  
Author(s):  
Can Yang ◽  
Zheng Chen ◽  
Bin Yao ◽  
Bobo Helian
Keyword(s):  
High Speed ◽  
Order Approximation ◽  
Contour Error ◽  
Coordinate Frame ◽  
Robust Controller ◽  
Contouring Control ◽  
Modeling Uncertainties ◽  
False Position ◽  
First Order Approximation ◽  
Control Application

Abstract In this paper, a strictly defined new orthogonal global task coordinate frame (NGTCF) based on the false position method is proposed for precision contouring control of biaxial systems. In contrast to the existed global task coordinate frame (GTCF), the value of the normal coordinate in NGTCF directly represents the contour error, rather than the first-order approximation. Moreover, different from the conventional GTCF just suitable for contours with explicit shape functions, the proposed NGTCF can be utilized in various complex contours. The false position method is adopted to calculate the curve coordinates of actual points in NGTCF. Then an adaptive robust controller (ARC) is designed to deal with the effects of strong coupling of the system dynamics in the task space and modeling uncertainties. The proposed NGTCF-based ARC contouring control strategy is tested on a linear motor driven biaxial industrial gantry. Experiments under different contouring tasks with high-speed and large-curvature are conducted to verify the effectiveness of the proposed method, and the experimental results confirm that the excellent contouring performance of the proposed approach can be achieved.

Dynamic Responses of Supercavitating Vehicles under Non-Stationary Random Excitation

2012 ◽  
Vol 591-593 ◽  
pp. 1934-1937
Author(s):  
Xiang Hua Song ◽  
Guang Ping Zou ◽  
Wei Guang An
Keyword(s):  
High Speed ◽  
Integration Method ◽  
Random Excitation ◽  
State Equation ◽  
Dynamic Responses ◽  
State Equations ◽  
Precise Integration ◽  
Supercavitating Vehicles ◽  
Structural Responses ◽  
First Moment

When the front end of the supercavitating vehicles subjects to very large axial non-stationary random excitation at high speed motion under water, it is necessary to analyze dynamic responses of supercavitating vehicles under non-stationary random excitation. The dynamical equation of supercavitating vehicles is transformed into the form of state equations. The Simpson integration method is going to calculate the integral term of the general solution of state equation to improve the precise integration method. The explicit expression of dynamic responses of supercavitating vehicles is deduced, the means and variances of structural responses are calculated with operation laws of the first moment and second moment. Under different sailing speeds and different cone-cavitator angles dynamic responses of supercavitating vehicles are given by the examples, and the effectiveness of the method was demonstrated.

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