A Rapid Approach for Calculating the Damped Eigenvalues of a Gas Turbine on a Minicomputer: Theory

1984 ◽  
Vol 106 (2) ◽  
pp. 239-249 ◽  
Author(s):  
E. J. Gunter ◽  
R. R. Humphris ◽  
H. Springer
Keyword(s):  
Gas Turbine ◽  
Characteristic Polynomial ◽  
Normal Modes ◽  
Complex Matrix ◽  
Large Computer ◽  
Mainframe Computer ◽  
The Matrix ◽  
Rigid Body Modes ◽  
Transfer Method ◽  
Matrix Transfer Method

The calculation of the damped eigenvalues of a large multistation gas turbine by the complex matrix transfer procedure may encounter numerical difficulties, even on a large computer due to numerical round-off errors. In this paper, a procedure is presented in which the damped eigenvalues may be rapidly and accurately calculated on a minicomputer with accuracy which rivals that of a mainframe computer using the matrix transfer method. The method presented in this paper is based upon the use of constrained normal modes plus the rigid body modes in order to generate the characteristic polynomial of the system. The constrained undamped modes, using the matrix transfer process with scaling, may be very accurately calculated for a multistation turbine on a minicomputer. In this paper, a five station rotor is evaluated to demonstrate the procedure. A method is presented in which the characteristic polynomial may be automatically generated by Leverrier’s algorithm. The characteristic polynomial may be directly solved or the coefficients of the polynomial may be examined by the Routh criteria to determine stability. The method is accurate and easy to implement on a 16 bit minicomputer.

The Solution and Parameter Analysis of the Single Pile Response Subject to Lateral Load Based on Three-Parameter Subgrade Resisting Force Model

2014 ◽  
Vol 711 ◽  
pp. 503-509
Author(s):  
Qian Fu ◽  
Jia Hao Huang ◽  
Shu Ting Liang ◽  
Xiao Qing Sun
Keyword(s):  
Finite Element ◽  
Lateral Load ◽  
Parameter Analysis ◽  
Force Model ◽  
Single Pile ◽  
Subgrade Reaction ◽  
The Matrix ◽  
Parametric Studies ◽  
Transfer Method ◽  
Matrix Transfer Method

To further investigate the mechanism of the interaction between the response of single pile and pile-soil on the condition of lateral load, on the basis of the normal type of the coefficient of subgrade reaction, this paper reaches the transfer matrix solution of single pile subject to lateral load by combining matrix transfer method with finite element method assuming that the coefficient of subgrade reaction is constant in each finite element. With the matrix solutions obtained, a computer program is developed using MATLAB to compute the pile responses and parametric studies are carried out on the effect of the constraint conditions of pile head and tip, effect of soil properties etc. and the results are discussed in detail.

scholarly journals The normalized distance Laplacian

2021 ◽  
Vol 9 (1) ◽  
pp. 1-18
Author(s):  
Carolyn Reinhart
Keyword(s):  
Spectral Radius ◽  
Characteristic Polynomial ◽  
Adjacency Matrix ◽  
Connected Graph ◽  
Distance Matrix ◽  
Laplacian Matrix ◽  
Diagonal Matrix ◽  
The Matrix

Abstract The distance matrix 𝒟(G) of a connected graph G is the matrix containing the pairwise distances between vertices. The transmission of a vertex vi in G is the sum of the distances from vi to all other vertices and T(G) is the diagonal matrix of transmissions of the vertices of the graph. The normalized distance Laplacian, 𝒟𝒧(G) = I−T(G)−1/2 𝒟(G)T(G)−1/2, is introduced. This is analogous to the normalized Laplacian matrix, 𝒧(G) = I − D(G)−1/2 A(G)D(G)−1/2, where D(G) is the diagonal matrix of degrees of the vertices of the graph and A(G) is the adjacency matrix. Bounds on the spectral radius of 𝒟 𝒧 and connections with the normalized Laplacian matrix are presented. Twin vertices are used to determine eigenvalues of the normalized distance Laplacian. The distance generalized characteristic polynomial is defined and its properties established. Finally, 𝒟𝒧-cospectrality and lack thereof are determined for all graphs on 10 and fewer vertices, providing evidence that the normalized distance Laplacian has fewer cospectral pairs than other matrices.

Simultaneous Determination of Eight New Generation Amide Insecticide Residues in Complex Matrix Agri-food by Multi-walled Carbon Nanotube Cleanup and UPLC-MS/MS

2021 ◽  
Author(s):  
Tao Lin ◽  
Xinglian Chen ◽  
Li Wang ◽  
Haixian Fang ◽  
Maoxuan Li ◽  
...  
Keyword(s):  
Mass Spectrometry ◽  
Simultaneous Determination ◽  
High Performance ◽  
Rapid Determination ◽  
Complex Matrix ◽  
Limit Of Quantification ◽  
Relative Standard ◽  
The Matrix ◽  
Multi Walled Carbon Nanotubes

Abstract The simultaneous determination method of 8 amide pesticides by multi-walled carbon nanotubes (MWCNs) cleanup, combined with QuEChERS method and ultra-high performance liquid chromatography-triple quadrupole tandem mass spectrometry has been developed and successfully applied in complex matrix such as green onions, celery, leeks, citrus, lychees, avocado. The matric effect of MWCNs is optimized and compared with QuEChERS materials. The results show that MWCNs can effectively reduce the matrix effect in sample extraction. The mass spectrometry is optimized, through their chemical structure skeletons, the ESI+ and ESI- mode are simultaneously scanned in the method. The coefficient (r) is greater than 0.9990, the limit of quantification ranges from 0.03 to 0.80 μg/kg, the recovery rate ranges from 71.2% to 120%, and the relative standard deviation (RSD) ranges from 3.8% to 9.4%. The method is fast, simple, sensitive, and has good purification effect. It is suitable for the rapid determination of amide pesticides in complex matrix agri-food.

On Solutions of Inverse Problem for Hermitian Generalized Hamiltonian Matrices

2013 ◽  
Vol 860-863 ◽  
pp. 2727-2731
Author(s):  
Kai Fu Liang ◽  
Ming Jun Li ◽  
Ze Lin Zhu
Keyword(s):  
Inverse Problem ◽  
Inverse Problems ◽  
Design Automation ◽  
Sufficient Conditions ◽  
Matrix Equations ◽  
Complex Matrix ◽  
Linear Quadratic ◽  
Real Representation ◽  
The Matrix ◽  
Necessary And Sufficient

Hamiltonian matrices have many applications to design automation and autocontrol, in particular in the linear-quadratic autocontrol problem. This paper studies the inverse problems of generalized Hamiltonian matrices for matrix equations. By real representation of complex matrix, we give the necessary and sufficient conditions for the existence of a Hermitian generalized Hamiltonian solutions to the matrix equations, and then derive the representation of the general solutions.

Low-Leakage Modular Regenerators for Gas-Turbine Engines

1997 ◽  
Author(s):  
James Anthony Kluka ◽  
David Gordon Wilson
Keyword(s):  
Gas Turbine ◽  
Gas Turbines ◽  
Turbine Engines ◽  
Gas Turbine Engines ◽  
Regenerative Heat ◽  
Turbine Engine ◽  
Low Leakage ◽  
The Matrix ◽  
Potential Applications ◽  
Ceramic Honeycomb

One of the significant problems plaguing regenerator designs is seal leakage resulting in a reduction of thermal efficiency. This paper describes the preliminary design and analysis of a new regenerative heat-exchanger concept, called a modular regenerator, that promises to provide improved seal-leakage performance. The modular regenerator concept consists of a ceramic-honeycomb matrix discretized into rectangular blocks, called modules. Separating the matrix into modules substantially reduces the transverse sealing lengths and substantially increases the longitudinal sealing lengths as compared with typical rotary designs. Potential applications can range from small gas-turbine engines for automotive applications to large stationary gas turbines for industrial power generation. Descriptions of two types of modular regenerators are presented including sealing concepts. Results of seal leakage analysis for typical modular regenerators sized for a small gas-turbine engine (120 kW) predict leakage rates under one percent for most seal-clearance heights.

scholarly journals Involvement of Crawling and Attached Ciliates in the Aggregation of Particles in Wastewater Treatment Plants

2008 ◽  
Vol 1 ◽  
pp. ASWR.S752 ◽  
Author(s):  
Lucía Arregui ◽  
María Linares ◽  
Blanca Pέrez-Uz ◽  
Almudena Guinea ◽  
Susana Serrano
Keyword(s):  
Wastewater Treatment ◽  
Extracellular Polymeric Substances ◽  
Wastewater Treatment Plants ◽  
Biological Activities ◽  
Feeding Strategies ◽  
Complex Matrix ◽  
Active Secretion ◽  
Latex Beads ◽  
The Matrix

The biological community in activated sludge wastewater plants is organized within this ecosystem as bioaggregates or flocs, in which the biotic component is embedded in a complex matrix comprised of extracellular polymeric substances mainly of microbial origin. The aim of this work is to study the role of different floc-associated ciliates commonly reported in wastewater treatment plants-crawling Euplotes and sessile Vorticella- in the formation of aggregates. Flocs, in experiments with ciliates and latex beads, showed more compactation and cohesion among particles than those in the absence of ciliates. Ciliates have been shown to contribute to floc formation through different mechanisms such as the active secretion of polymeric substances (extrusomes), their biological activities (movement and feeding strategies), or the cysts formation capacity of some species. Staining with lectins coupled to fluorescein showed that carbohydrate of the matrix contained glucose, manose, N-acetyl-glucosamine and galactose. Protein fraction revealed over the latex beads surfaces could probably be of bacterial origin, but nucleic acids represented an important fraction of the extracellular polymeric substances of ciliate origin.

Eigenvalue localization for complex matrices

2014 ◽  
Vol 27 ◽  
Author(s):  
Ibrahim Gumus ◽  
Omar Hirzallah ◽  
Fuad Kittaneh
Keyword(s):  
Frobenius Norm ◽  
Complex Matrix ◽  
Complex Matrices ◽  
Eigenvalue Localization ◽  
The Matrix

Let $A$ be an $n\times n$ complex matrix with $n\geq 3$. It is shown that at least $n-2$ of the eigenvalues of $A$ lie in the disk \begin{equation*}\left\vert z-\frac{\func{tr}A}{n}\right\vert \leq \sqrt{\frac{n-1}{n}\left(\sqrt{\left( \left\Vert A\right\Vert _{2}^{2}-\frac{\left\vert \func{tr} A\right\vert ^{2}}{n}\right) ^{2}-\frac{\left\Vert A^{\ast }A-AA^{\ast}\right\Vert _{2}^{2}}{2}}-\frac{\limfunc{spd}\nolimits^{2}(A)}{2}\right) },\end{equation*} where $\left\Vert A\right\Vert _{2},$ $\func{tr}A$, and $\limfunc{spd}(A)$ denote the Frobenius norm, the trace, and the spread of $A$, respectively. In particular, if $A=\left[ a_{ij}\right] $ is normal, then at least $n-2$ of the eigenvalues of $A$ lie in the disk {\small \begin{eqnarray*} & & \left\vert z-\frac{\func{tr}A}{n}\right\vert \\ & & \leq \sqrt{\frac{n-1}{n}\left( \frac{\left\Vert A\right\Vert _{2}^{2}}{2}-\frac{\left\vert \func{tr}A\right\vert ^{2}}{n}-\frac{3}{2}\max_{i,j=1,\dots,n} \left( \sum_{\substack{ k=1 \\ k\neq i}}^{n}\left\vert a_{ki}\right\vert ^{2}+\sum_{\substack{ k=1 \\ k\neq j}}^{n}\left\vert a_{kj}\right\vert ^{2}+\frac{\left\vert a_{ii}-a_{jj}\right\vert ^{2}}{2}\right) \right) }. \end{eqnarray*}} Moreover, the constant $\frac{3}{2}$ can be replaced by $4$ if the matrix $A$ is Hermitian.

scholarly journals Approximating the Matrix Sign Function Using a Novel Iterative Method

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
F. Soleymani ◽  
P. S. Stanimirović ◽  
S. Shateyi ◽  
F. Khaksar Haghani
Keyword(s):  
Iterative Method ◽  
Asymptotical Stability ◽  
Complex Matrix ◽  
Initial Matrix ◽  
Matrix Sign Function ◽  
Sign Function ◽  
The Matrix ◽  
Square Complex

This study presents a matrix iterative method for finding the sign of a square complex matrix. It is shown that the sequence of iterates converges to the sign and has asymptotical stability, provided that the initial matrix is appropriately chosen. Some illustrations are presented to support the theory.

Symbolic Computation of Inverse Kinematics for General 6R Manipulators Based on Raghavan and Roth’s Solution

2020 ◽  
Author(s):  
Keisuke Arikawa
Keyword(s):  
Characteristic Polynomial ◽  
Symbolic Computation ◽  
Inverse Kinematics ◽  
Structural Parameters ◽  
Efficient Computation ◽  
Joint Angles ◽  
Arbitrary Geometries ◽  
The Matrix ◽  
Rational Polynomials ◽  
Symbolic Constraints

Abstract We discuss the symbolic computation of inverse kinematics for serial 6R manipulators with arbitrary geometries (general 6R manipulators) based on Raghavan and Roth’s solution. The elements of the matrices required in the solution were symbolically calculated. In the symbolic computation, an algorithm for simplifying polynomials upon considering the symbolic constraints (constraints of the trigonometric functions and those of the rotation matrix), a method for symbolic elimination of the joint variables, and an efficient computation of the rational polynomials are presented. The elements of the matrix whose determinant produces a 16th-order single variable polynomial (characteristic polynomial) were symbolically calculated by using structural parameters (parameters that define the geometry of the manipulator) and hand configuration parameters (parameters that define the hand configuration). The symbolic determinant of the matrix consists of huge number of terms even when each element is replaced by a single symbol. Instead of expressing the coefficients in a characteristic polynomial by structural parameters and hand configuration parameters, we substituted appropriate rational numbers that strictly satisfy the constraints of the symbols for the elements of the matrix and calculated the determinant (numerical error free calculation). By numerically calculating the real roots of the rational characteristic polynomial and the joint angles for each root, we verified the formulation for the symbolic computation.

Pseudo-Tournament Matrices and Their Eigenvalues

2014 ◽  
Vol 4 (3) ◽  
pp. 205-221
Author(s):  
Chuanlong Wang ◽  
Xuerong Yong
Keyword(s):  
Directed Graph ◽  
Round Robin ◽  
Column Vector ◽  
Complex Matrix ◽  
The Matrix ◽  
Tournament Matrices ◽  
Class Of Matrices

AbstractA tournament matrix and its corresponding directed graph both arise as a record of the outcomes of a round robin competition. An n × n complex matrix A is called h-pseudo-tournament if there exists a complex or real nonzero column vector h such that A + A* = hh* − I. This class of matrices is a generalisation of well-studied tournament-like matrices such as h-hypertournament matrices, generalised tournament matrices, tournament matrices, and elliptic matrices. We discuss the eigen-properties of an h-pseudo-tournament matrix, and obtain new results when the matrix specialises to one of these tournament-like matrices. Further, several results derived in previous articles prove to be corollaries of those reached here.

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