Broadband vibration control using passive circuits in the matrix-second order framework

2001 ◽  
Author(s):  
Seung-Keon Kwak ◽  
Gregory N. Washington
Keyword(s):  
Vibration Control ◽  
Second Order ◽  
Passive Circuits ◽  
The Matrix

Weighted Averaging Techniques in Oscillation Theory for Second Order Difference Equations

1992 ◽  
Vol 35 (1) ◽  
pp. 61-69 ◽  
Author(s):  
Lynn H. Erbe ◽  
Pengxiang Yan
Keyword(s):  
Oscillation Theory ◽  
Second Order ◽  
Weighted Averaging ◽  
Real Numbers ◽  
Order Difference ◽  
The Matrix ◽  
System 2 ◽  
Oscillation And Nonoscillation Criteria ◽  
Oscillation And Nonoscillation ◽  
Averaging Techniques

AbstractWe consider the self-adjoint second-order scalar difference equation (1) Δ(rnΔxn) +pnXn+1 = 0 and the matrix system (2) Δ(RnΔXn) + PnXn+1 = 0, where are seQuences of real numbers (d x d Hermitian matrices) with rn > 0(Rn > 0). The oscillation and nonoscillation criteria for solutions of (1) and (2), obtained in [3, 4, 10], are extended to a much wider class of equations by Riccati and averaging techniques.

scholarly journals On the Parametric Solution to the Second-Order Sylvester Matrix EquationEVF2−AVF−CV=BW

2007 ◽  
Vol 2007 ◽  
pp. 1-16 ◽  
Author(s):  
Wang Guo-Sheng ◽  
Lv Qiang ◽  
Duan Guang-Ren
Keyword(s):  
Control Systems ◽  
Matrix Equation ◽  
Second Order ◽  
Diagonal Form ◽  
Sylvester Matrix Equation ◽  
Parametric Solution ◽  
Design Problems ◽  
Analysis And Design ◽  
Sylvester Matrix ◽  
The Matrix

This paper considers the solution to a class of the second-order Sylvester matrix equationEVF2−AVF−CV=BW. Under the controllability of the matrix triple(E,A,B), a complete, general, and explicit parametric solution to the second-order Sylvester matrix equation, with the matrixFin a diagonal form, is proposed. The results provide great convenience to the analysis of the solution to the second-order Sylvester matrix equation, and can perform important functions in many analysis and design problems in control systems theory. As a demonstration, an illustrative example is given to show the effectiveness of the proposed solution.

Retardation in non-dispersive interactions between molecules

1966 ◽  
Vol 295 (1443) ◽  
pp. 476-489 ◽  
Keyword(s):  
Quantum Electrodynamics ◽  
Exchange Interactions ◽  
Dipole Interaction ◽  
Second Order ◽  
The Other ◽  
Spin Orbit ◽  
Wave Zone ◽  
Expectation Value ◽  
Near Zone ◽  
The Matrix

The second order T matrix corresponding to the interaction between two molecules is calculated by quantum electrodynamics. In the near zone the matrix reduces to the expectation value of the Breit Hamiltonian for the two-centre problem. In the wave zone a retarded Briet operator is found for exchange interactions. A reduction to the Pauli limit is made. The interactions are discussed severally for the spin-spin, (spin-dipole)-(spin-dipole), spin-orbit and dipole-(spin-dipole) cases. At large separations the T matrix is complex and the imaginary parts, previously given for the dipole-dipole interaction, are found for the other cases.

A broadband vibration control using passive circuits

2003 ◽  
Author(s):  
Gregory N. Washington ◽  
Matt Detrick ◽  
Seung-Keon Kwak
Keyword(s):  
Vibration Control ◽  
Passive Circuits

The multi-body analysis and vibration control of the second-order mode of a hoop flexible structure

2017 ◽  
Vol 230 (4) ◽  
pp. 1377-1386 ◽  
Author(s):  
Guoliang Ma ◽  
Minglong Xu ◽  
Tao Liu ◽  
Yajun Luo
Keyword(s):  
Vibration Control ◽  
Second Order ◽  
Flexible Structure ◽  
Order Mode ◽  
Multi Body

scholarly journals Characterization of Homogeneous System of Difference Equations

2021 ◽  
Vol 32 (1) ◽  
pp. 25
Author(s):  
Huda Hussein Abed ◽  
Bassam Jabbar Al-Asadi
Keyword(s):  
Difference Equations ◽  
Homogeneous System ◽  
Second Order ◽  
System Of Difference Equations ◽  
The Matrix

In this paper, we introduced new definitions of the system of homogenous difference equations of order two; namely homogenous and semi homogenous system, where we focused on finding the equivalents for these definitions of order one as well as of order greater than one for the system of difference equations of the second order and given some examples. We also a given formula to find the power of the matrix that we used in this research.

scholarly journals Partial Eigenvalue Assignment for Gyroscopic Second-Order Systems with Time Delay

Mathematics ◽  
2020 ◽  
Vol 8 (8) ◽  
pp. 1235
Author(s):  
Hao Liu ◽  
Ranran Li ◽  
Yingying Ding
Keyword(s):  
Time Delay ◽  
Lower Order ◽  
Assignment Problem ◽  
Hadamard Product ◽  
Second Order ◽  
Step Method ◽  
Computational Costs ◽  
The Matrix ◽  
Second Order Systems ◽  
Eigenvalue Assignment

In this paper, the partial eigenvalue assignment problem of gyroscopic second-order systems with time delay is considered. We propose a multi-step method for solving this problem in which the undesired eigenvalues are moved to desired values and the remaining eigenvalues are required to remain unchanged. Using the matrix vectorization and Hadamard product, we transform this problem into a linear systems of lower order, and analysis the computational costs of our method. Numerical results exhibit the efficiency of our method.

scholarly journals Algorithms for Solving Nonhomogeneous Generalized Sylvester Matrix Equations

2020 ◽  
Vol 2020 ◽  
pp. 1-5
Author(s):  
Ehab A. El-Sayed ◽  
Eid E. El Behady
Keyword(s):  
Explicit Solution ◽  
Second Order ◽  
New Method ◽  
Matrix Equations ◽  
Numerical Examples ◽  
First Order ◽  
Hessenberg Form ◽  
Sylvester Matrix ◽  
The Matrix ◽  
Sylvester Matrix Equations

This paper considers a new method to solve the first-order and second-order nonhomogeneous generalized Sylvester matrix equations AV+BW= EVF+R and MVF2+DV F+KV=BW+R, respectively, where A,E,M,D,K,B, and F are the arbitrary real known matrices and V and W are the matrices to be determined. An explicit solution for these equations is proposed, based on the orthogonal reduction of the matrix F to an upper Hessenberg form H. The technique is very simple and does not require the eigenvalues of matrix F to be known. The proposed method is illustrated by numerical examples.

Elastic wave propagation using fully vectorized high order finite‐difference algorithms

Geophysics ◽  
1992 ◽  
Vol 57 (2) ◽  
pp. 218-232 ◽  
Author(s):  
A. Vafidis ◽  
F. Abramovici ◽  
E. R. Kanasewich
Keyword(s):  
Finite Difference ◽  
Elastic Wave ◽  
Second Order ◽  
Finite Difference Schemes ◽  
Difference Operators ◽  
Two Dimensional ◽  
Elastic Wave Equation ◽  
The Matrix ◽  
Comparison Of The Results ◽  
High Order Finite Difference

Two finite‐difference schemes for solving the elastic wave equation in heterogeneous two‐dimensional media are implemented on a vector computer. A modified Lax‐Wendroff scheme that is second‐order accurate both in time and space and is a version of the MacCormack scheme that is second‐order accurate in time and fourth‐order in space. The algorithms are based on the matrix times vector by diagonals technique that is fully vectorized and is described using a novel notation for vector supercomputer operations. The technique described can be implemented on a vector processor of modest dimensions and increase the applicability of finite differences. The two difference operators are compared and the programs are tested for a simple case of standing sinusoidal waves for which the exact solution is known and also for a two‐layer model with a line source. A comparison of the results for an actual well‐to‐well experiment verifies the usefulness of the two‐dimensional approach in modeling the results.

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