Finite iterative method for solving coupled Sylvester-transpose matrix equations

2014 ◽  
Vol 46 (1-2) ◽  
pp. 351-372 ◽  
Author(s):  
Caiqin Song ◽  
Jun-e Feng ◽  
Xiaodong Wang ◽  
Jianli Zhao
Keyword(s):  
Iterative Method ◽  
Matrix Equations ◽  
Finite Iterative Method

An Iterative Method for the Displacement Analysis of Spatial Mechanisms

1964 ◽  
Vol 31 (2) ◽  
pp. 309-314 ◽  
Author(s):  
J. J. Uicker ◽  
J. Denavit ◽  
R. S. Hartenberg
Keyword(s):  
Iterative Method ◽  
Complete Solution ◽  
Algebraic Method ◽  
Matrix Equations ◽  
Displacement Analysis ◽  
Spatial Mechanisms ◽  
Symbolic Notation ◽  
The Matrix ◽  
The Subject ◽  
Computer Operation

An algebraic method for the displacement analysis of linkages has been the subject of earlier publications [1, 2]. This method, based on the use of a symbolic notation, allows the application of matrix algebra to the study of displacements in linkages, and permits formulation of all the kinematic relations of a linkage in terms of matrix equations. Based on this earlier work, the present paper develops an iterative method for the solution of the matrix equations required in displacement analysis. A complete solution is given for simple-closed linkages consisting of revolute and prismatic pairs (and their combinations). A brief indication of how higher pairs and multiple-closed chains may be handled is also given. Particularly useful in spatial problems, since it does not depend on visualization, this approach is developed in a manner intended for digital-computer operation.

Calculation of the Natural Frequencies of Transverse Vibration of Complex Beams Using the Differential-Matrix Equations

2011 ◽  
Vol 243-249 ◽  
pp. 284-289
Author(s):  
Yu Zhang
Keyword(s):  
Iterative Method ◽  
Boundary Conditions ◽  
Cross Section ◽  
Transverse Vibration ◽  
Natural Frequencies ◽  
Composite Beams ◽  
Matrix Equations ◽  
Generalized Differential ◽  
Set Up ◽  
Differential Matrix

The generalized differential-matrix equations of transverse vibration of the beams were set up and they were solved by means of Cauchy sequence iterative method. Then according to the boundary conditions at two ends of the beams the natural frequencies of the transverse vibration of the different beams including the complex beams of non-uniform section and composite beams under different boundary conditions were figured out. The form of the differential-matrix is simple. The calculation of the sequence iterations can be accomplished by simple computer program. Using the method in this paper, the amount of work of calculation is reduced greatly and the results are accurate compared with the approximate method in which a beam of non-uniform section is replaced by many small segments of equal cross-section.

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