scholarly journals High Efficiency Computation of the Variances of Structural Evolutionary Random Responses

2000 ◽  
Vol 7 (4) ◽  
pp. 209-216 ◽  
Author(s):  
J.H. Lin ◽  
D.K. Sun ◽  
W.X. Zhong ◽  
W.S. Zhang
Keyword(s):  
High Efficiency ◽  
Integration Method ◽  
Random Noise ◽  
Lyapunov Equations ◽  
Precise Integration ◽  
Precise Integration Method ◽  
Random Responses ◽  
Differential Lyapunov Equations

For structures subjected to stationary or evolutionary white/colored random noise, their various response variances satisfy algebraic or differential Lyapunov equations. The solution of these Lyapunov equations used to be very difficult. A precise integration method is proposed in the present paper, which solves such Lyapunov equations accurately and very efficiently.

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.

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