Derivations of Major Coupling Derivatives, and the State Space Formulation, of the Coupled Equations of Motion

2006 ◽  
Author(s):  
Mohammad Sadraey ◽  
Richard Colgren
Keyword(s):  
State Space ◽  
Equations Of Motion ◽  
The State ◽  
Coupled Equations ◽  
Space Formulation

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.

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.

Analytical Investigation of Aero-Elastic Behavior of Aircraft Composite Box Wings in Unsteady Compressible Flow

2011 ◽  
Author(s):  
T. Farsadi ◽  
H. Haddadpour ◽  
U. Yuceoglu
Keyword(s):  
State Space ◽  
Compressible Flow ◽  
Separation Of Variables ◽  
Equations Of Motion ◽  
Analytical Investigation ◽  
The State ◽  
Elastic Behavior ◽  
Aeroelastic System ◽  
The Time Domain ◽  
Flight Regimes

In this study, an anisotropic thin-walled “Composite Box Beam” as the “Wing System” is used to consider the effects of the fiber orientation and the lay-up configuration on the aeroelastic stability and the dynamic response of an aircraft wing. The present “Circumferentially Asymmetric Stiffness Model (CAS)” takes into account a group of non-classical effects; such as the transverse shear, the material anisotropy, warping inhibition, etc. The “Aerodynamic Strip Method” based on “Wagner Functions” in unsteady compressible flow are used to simulate compressible unsteady aerodynamic effects in the “state space” form. In addition, the mass, the stiffness and the damping matrices of the present non-conservative aeroelastic system are formed so that, the “Extended Galerkin’s Method (EGM)” and the “Separation of Variables Method” can be employed. As a result, the coupled and linear “Governing System of Dynamic Equations” are obtained. After then, by transforming matrices into the “state space” and “state vector” forms, the problem under study is finally converted into an “Eigenvalue Problem and Analysis”. Hence, the “flutter” and the “divergence” speeds for various layer configurations with different geometric and material properties and fiber orientations were obtained. Furthermore, by solving the aforementioned equations of motion in the time domain, the aeroelastic responses of the “Composite Box Wing System” for different flight regimes are computed. The present numerical results were compared and are verified with some existing experimental results in the literature. Based on these, some brief but important conclusions are presented.

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.

scholarly journals New Method of State-Space Formulation for Degenerate Circuit and Coupling Circuit

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Chung-Cheng Chen ◽  
Jian Ke ◽  
Yen-Ting Chen
Keyword(s):  
Differential Equation ◽  
State Space ◽  
State Equation ◽  
The State ◽  
New Method ◽  
Equation Approach ◽  
Electrical Field ◽  
Coupling Circuit ◽  
Space Formulation ◽  
Traditional Approaches

The state-space formulation overcomes many limitations of traditional differential equation approach and is utilized as alternative to many traditional approaches in the modern electrical field. This paper proposes a new method of finding the state equation for degenerate circuit and coupling circuit that have not been systematically solved now. This paper also introduces some sound improvements to solve complicated dependent-source circuits. Four comparative examples are demonstrated to show the significant merits that our method owns over the traditional approaches.

scholarly journals Cohort effects in mortality modelling: a Bayesian state-space approach

2018 ◽  
Vol 13 (1) ◽  
pp. 109-144
Author(s):  
Man Chung Fung ◽  
Gareth W. Peters ◽  
Pavel V. Shevchenko
Keyword(s):  
State Space ◽  
Empirical Studies ◽  
The State ◽  
Cohort Effects ◽  
Modelling Framework ◽  
Mortality Models ◽  
Mortality Modelling ◽  
Space Formulation ◽  
Mortality Forecasts ◽  
Generalised Linear Modelling

AbstractCohort effects are important factors in determining the evolution of human mortality for certain countries. Extensions of dynamic mortality models with cohort features have been proposed in the literature to account for these factors under the generalised linear modelling framework. In this paper we approach the problem of mortality modelling with cohort factors incorporated through a novel formulation under a state-space methodology. In the process we demonstrate that cohort factors can be formulated naturally under the state-space framework, despite the fact that cohort factors are indexed according to year-of-birth rather than year. Bayesian inference for cohort models in a state-space formulation is then developed based on an efficient Markov chain Monte Carlo sampler, allowing for the quantification of parameter uncertainty in cohort models and resulting mortality forecasts that are used for life expectancy and life table constructions. The effectiveness of our approach is examined through comprehensive empirical studies involving male and female populations from various countries. Our results show that cohort patterns are present for certain countries that we studied and the inclusion of cohort factors are crucial in capturing these phenomena, thus highlighting the benefits of introducing cohort models in the state-space framework. Forecasting of cohort models is also discussed in light of the projection of cohort factors.

Modeling of CCLP in koryo extract production

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Ji Chol ◽  
Ri Jun Il
Keyword(s):  
Process Control ◽  
Medical Care ◽  
State Space ◽  
State Space Model ◽  
The State ◽  
Space Model ◽  
Effective Components ◽  
Counter Current

Abstract The modeling of counter-current leaching plant (CCLP) in Koryo Extract Production is presented in this paper. Koryo medicine is a natural physic to be used for a diet and the medical care. The counter-current leaching method is mainly used for producing Koryo medicine. The purpose of the modeling in the previous works is to indicate the concentration distributions, and not to describe the model for the process control. In literature, there are no nearly the papers for modeling CCLP and especially not the presence of papers that have described the issue for extracting the effective components from the Koryo medicinal materials. First, this paper presents that CCLP can be shown like the equivalent process consisting of two tanks, where there is a shaking apparatus, respectively. It allows leachate to flow between two tanks. Then, this paper presents the principle model for CCLP and the state space model on based it. The accuracy of the model has been verified from experiments made at CCLP in the Koryo Extract Production at the Gang Gyi Koryo Manufacture Factory.

Sign in / Sign up

Export Citation Format

Share Document