Decomposition of time-varying LC elements and the state-space formulation

1969 ◽  
Vol 5 (7) ◽  
pp. 142 ◽  
Author(s):  
T. Murata
Keyword(s):  
State Space ◽  
The State ◽  
Time Varying ◽  
Space Formulation

A method for deriving a non-singular state-space formulation based on Rubin's model for Pogo analysis

2018 ◽  
Vol 233 (8) ◽  
pp. 2717-2730
Author(s):  
Shujun Tan ◽  
Qingwei Wang ◽  
Zhigang Wu ◽  
Yunfei Yang ◽  
Ziwen Yu
Keyword(s):  
State Space ◽  
State Space Model ◽  
The State ◽  
Dynamic Equations ◽  
Time Varying ◽  
The Finite Element Method ◽  
Space Model ◽  
Assembly Method ◽  
Standard Manner ◽  
Space Formulation

A method for deriving a non-singular state-space formulation based on Rubin's model for Pogo analysis is presented in this study. Because of the non-singularity, the state-space model can be directly used in frequency-domain analyses and time-domain simulations. To describe the assembly method concisely, the dynamic equations of the nine types of independent elements are described in a standard manner. The nine types of elements are divided into two classes according to characteristics of the dynamic equations. The mapping relationship between the local and global numbers of elements and nodes is obtained by numbering all of the elements and nodes. By integrating the element stiffness matrixes to obtain the total stiffness matrix used in the finite element method, the coefficient matrixes of the improved Rubin's model are assembled from the coefficient matrixes of all of the elements according to the mapping relationship. Based on the non-singular model, the time-varying simulation with the nonlinear property of the accumulator can be done conveniently by revising the state-space model. The successful application of this method to a Pogo analysis of a certain type of CZ rocket used in China verifies the correctness and efficiency of the method of this study.

Cylindrically Anisotropic Tubes Containing a Line Dislocation

2006 ◽  
Author(s):  
Chung-Hao Wang
Keyword(s):  
State Space ◽  
Dislocation Line ◽  
Longitudinal Axis ◽  
The State ◽  
Fourier Series Expansion ◽  
General Solutions ◽  
Mixed Dislocation ◽  
Line Dislocation ◽  
Space Formulation ◽  
Cylindrically Anisotropic

An analytical solution of the problem of a cylindrically anisotropic tube which contains a line dislocation is presented in this study. The state space formulation in conjunction with the eigenstrain theory is proved to be a feasible and systematic methodology to analyze a tube with the existence of dislocations. The state space formulation which expediently groups the displacements and the cylindrical surface traction can construct a governing differential matrix equation. By using Fourier series expansion and the well developed theory of matrix algebra, the asymmetrical solutions are not only explicit but also compact in form. The dislocation considered in this study is a kind of mixed dislocation which is the combination of edge dislocations and a screw dislocation and the dislocation line is parallel to the longitudinal axis of the tube. The degeneracy of the eigen relation and the technique to determine the inverse of a singular matrix are thoroughly discussed, so that the general solutions can be applied to the case of isotropic tubes, which is one of the novel features of this research. The results of isotropic problems, which are belong to the general solutions, are compared with the well-established expressions in the literature. The satisfied correspondences of these comparisons indicate the validness of this study. A cylindrically orthotropic tube is also investigated as an example and the numerical results for the displacements and tangential stress on the outer surface are displayed. The effects on surface stresses due to the existence of a dislocation appear to have a characteristic of localized phenomenon.

Response and Discretization Methods for Axially Moving Materials

1991 ◽  
Vol 44 (11S) ◽  
pp. S279-S284 ◽  
Author(s):  
J. A. Wickert ◽  
C. D. Mote
Keyword(s):  
State Space ◽  
Degrees Of Freedom ◽  
Equations Of Motion ◽  
Harmonic Excitation ◽  
The State ◽  
Space Formulation ◽  
Axially Moving ◽  
Effective Use ◽  
Gyroscopic Systems ◽  
Acceleration Component

Through a convective acceleration component, the equations of motion for axially-moving materials are skew-symmetric in the state space formulation, so that the response problem is best analyzed within the broader context of continuous gyroscopic systems. With particular application to the prototypical traveling string and beam models, a modal analysis that associates degrees of freedom with the complex state eigenfunctions and their conjugates is presented. This procedure is well-suited for harmonic excitation sources, and in some instances, it is more convenient than previous methods which decompose the modal coordinates, eigenfunctions, and generalized forces into real and imaginary components. Also from the state space perspective, Rayleigh’s quotient for gyroscopic systems provides a variational method for determining the eigensolutions of axially-moving materials. Ritz discretization of the quotient can make effective use of the speed-adapting modes of the traveling string and beam models as they are rich in phase, as well as amplitude, content.

Sign in / Sign up

Export Citation Format

Share Document