scholarly journals The split coefficient matrix method for hyperbolic systems of gasdynamic equations

1979 ◽  
Author(s):  
Sukumar Raman Chakravarthy
Keyword(s):  
Matrix Method ◽  
Hyperbolic Systems ◽  
Coefficient Matrix ◽  
Gasdynamic Equations

scholarly journals Membangkitkan Suatu Matriks Unimodular Dengan Python

2018 ◽  
Vol 5 (2) ◽  
pp. 1-9
Author(s):  
Samsul Arifin ◽  
Indra Bayu Muktyas
Keyword(s):  
Matrix Method ◽  
Coefficient Matrix ◽  
Inverse Matrix ◽  
Solution Vector ◽  
Unimodular Matrix ◽  
All Solutions ◽  
Cramer’S Rule

An SPL can be represented as a multiplication of the coefficient matrix and solution vector of the SPL. Determining the solution of an SPL can use the inverse matrix method and Cramer's rule, where both can use the concept of the determinant of a matrix. If the coefficient matrix is a unimodular matrix, then all solutions of an SPL are integers. In this paper we will present a method of generating a unimodular matrix using Python so that it can be utilized on an SPL. Keywords: SPL, Unimodular Matrix, Python

scholarly journals Free Vibration Characteristic of Multilevel Beam Based on Transfer Matrix Method of Linear Multibody Systems

2014 ◽  
Vol 6 ◽  
pp. 792478 ◽  
Author(s):  
Laith K. Abbas ◽  
Xiaoting Rui
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Matrix Method ◽  
Multibody Systems ◽  
Coefficient Matrix ◽  
Complex Structures ◽  
Vibration Characteristic ◽  
Boundary State ◽  
Novel Algorithms

In this paper, an approach based on transfer matrix method of linear multibody systems (MS-TMM) is developed to analyze the free vibration of a multilevel beam, coupled by spring/dashpot systems attached to them in-span. The Euler-Bernoulli model is used for the transverse vibration of the beams, and the spring/dashpot system represents a simplified model of a viscoelastic material. MS-TMM reduces the dynamic problem to an overall transfer equation which only involves boundary state vectors. The state vectors at the boundaries are composed of displacements, rotation angles, bending moments, and shear forces, which are partly known and partly unknown, and end up with reduced overall transfer matrix. Nontrivial solution requires the coefficient matrix to be singular to yield the required natural frequencies. This paper implements two novel algorithms based on the methodology by reducing the zero search of the reduced overall transfer matrix's determinate to a minimization problem and demonstrates a simple and robust algorithm being much more efficient than direct enumeration. The proposal method is easy to formulate, systematic to apply, and simple to code and can be extended to complex structures with any boundary conditions. Numerical results are presented to show the validity of the proposal method against the published literature.

Transfer Matrix Method for the Determination of the Free Vibration of Two Elastically Coupled Beams

2013 ◽  
Vol 372 ◽  
pp. 301-304 ◽  
Author(s):  
Laith K. Abbas ◽  
Dieter Bestle ◽  
Xiao Ting Rui
Keyword(s):  
Free Vibration ◽  
Transfer Matrix ◽  
Transfer Matrix Method ◽  
Transfer Equation ◽  
Matrix Method ◽  
Coefficient Matrix ◽  
The State ◽  
Discrete Elements ◽  
Numerical Result ◽  
Boundary State

The feasibility of using the transfer matrix method (TMM) to compute the free vibration characteristics of a system composed of continues and discrete elements vibrating in a plane is explored theoretically. In the approach to the problem, a general analytical method based on TMM is developed for the vibrations of two uniform Euler-Bernoulli beams coupled by a spring. The components of the transfer matrix are all functions of the systems natural frequency. The overall transfer equation only involves boundary state vectors, whereas the state vectors at all other connection points do not appear. The state vectors at the boundary are composed of displacements, rotation angles, bending moments and shear forces, which are partly known and partly unknown. Moreover, the overall transfer matrix is independent of the degrees of the freedom. A non-trivial solution of the final overall transfer equation requires the coefficient matrix to be singular. This paper reduces the zero search of its determinate to a minimization problem and demonstrates a simple, robust algorithm being much more efficient than direct enumeration. A numerical result is presented to demonstrate the proposal method.

scholarly journals A Study on Influence Coefficient Matrix Method

1985 ◽  
Vol 28 (240) ◽  
pp. 1077-1084
Author(s):  
Akiya SUGIMOTO
Keyword(s):  
Matrix Method ◽  
Coefficient Matrix ◽  
Influence Coefficient

scholarly journals Incremental holistic controller

2021 ◽  
Author(s):  
Alexander Weinmann
Keyword(s):  
Control System ◽  
State Space ◽  
Matrix Method ◽  
Coefficient Matrix ◽  
Design Element ◽  
Main Interest ◽  
Iterative Design ◽  
Performance Quality ◽  
Inverse Coefficient

AbstractThe trace of inverse coefficient matrix method in state space is used to implement and simplify an iterative design of a control system with main interest in increasing dynamical performance quality or to check if stability danger exists. The $\tau $ τ -locus is a helpful design element. Various applications and examples are presented for illustration.

scholarly journals Cell Arrangement Method for Solving Systems of Linear Equations in Three Unknown

2019 ◽  
pp. 1-8
Author(s):  
A. Adu-Sackey ◽  
G. O. Lartey ◽  
F. T. Oduro ◽  
Stephen Eduafo
Keyword(s):  
Matrix Method ◽  
Linear Equations ◽  
Coefficient Matrix ◽  
Simultaneous Equation ◽  
Cell Arrangement ◽  
Alternative Approach ◽  
Daunting Task ◽  
Systems Of Linear Equations ◽  
Lengthy Process

In this paper, we develop an approach for finding the cofactor, ad joint, determinant and inverse of a three by three matrix under the Cell Arrangements method using the coefficient matrix of a given systems of linear equation in three unknowns. The method takes out completely the seemingly daunting task in evaluating such matrices associated to the standard matrix method in solving simultaneous equation in three variable. Unlike the standard matrix method that goes through a lengthy process to obtain separately all the matrices necessary for the determination of the unknowns, the structural frame of the Cell Arrangement method comes in handy and are consistent with the results from systems that have unique solutions. This alternative approach provides all the vital hybrid matrices of the coefficient matrix needed in the determination of the unknowns of the system of equations in three variables. It is our view that by far, the Cell arrangement method is easy to work with and less prone to errors that are often connected with other known methods.

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