THE MARGINAL STABILITY OF AUTONOMOUS DIFFERENTIAL EQUATIONS

1993 ◽  
Vol 03 (03) ◽  
pp. 785-788
Author(s):  
N.N. GREENBAUN
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Nonlinear Differential Equations ◽  
Steady State Solution ◽  
Usual Method ◽  
State Solution ◽  
Marginal Stability ◽  
State Variables ◽  
Autonomous Differential Equations

Solutions in the vicinity of a steady state solution to a system of autonomous nonlinear differential equations are of interest to modelers. The usual method for determining marginal stability of the steady state is the Routh-Hurwitz criterion. The method offered here is less complicated and more efficient when the number of state variables exceeds three.

Frequency response analysis of periodically time varying circuits

2018 ◽  
Vol 37 (3) ◽  
pp. 1204-1213
Author(s):  
Igor Korotyeyev
Keyword(s):  
Steady State ◽  
Differential Equations ◽  
Steady State Solution ◽  
Variable Coefficients ◽  
State Solution ◽  
Response Analysis ◽  
Time Varying ◽  
Content Type ◽  
Frequency Responses ◽  
Definition Of

Purpose The purpose of this paper is to introduce a method for the analysis of steady-state processes in periodically time varying circuits. The method is based on a new definition of frequency responses for periodic time-varying circuits. Design/methodology/approach Processes in inverter circuits are often described by differential equations with periodically variable coefficients and forcing functions. To obtain a steady-state periodic solution, the expansion of differential equations into a domain of two independent variables of time is made. To obtain differential equations with constant coefficients the Lyapunov transformation is applied. The two-dimensional Laplace transform is used to find a steady-state solution. The steady-state solution is obtained in the form of the double Fourier series. The transfer function and frequency responses for the inverter circuit are introduced. Findings A set of frequency characteristics are defined. An example of a boost inverter is considered, and a set of frequency responses for voltage and current are presented. These responses show a resonance that is missed if the averaged state-space method is used. Originality/value A new definition of frequency responses is presented. On the basis of frequency responses, a modulation strategy and filters can be chosen to improve currents and voltages.

scholarly journals Algorithm for determining two-periodic steady-states in AC machines directly in time domain

2016 ◽  
Vol 65 (3) ◽  
pp. 575-583 ◽  
Author(s):  
Tadeusz J. Sobczyk
Keyword(s):  
Steady State ◽  
Time Domain ◽  
Nonlinear Differential Equations ◽  
Harmonic Balance Method ◽  
Steady State Solution ◽  
Steady States ◽  
State Solution ◽  
Time Interval ◽  
Ac Machines ◽  
Set Of Points

Abstract This paper describes an algorithm for finding steady states in AC machines for the cases of their two-periodic nature. The algorithm enables to specify the steady-state solution identified directly in time domain despite of the fact that two-periodic waveforms are not repeated in any finite time interval. The basis for such an algorithm is a discrete differential operator that specifies the temporary values of the derivative of the two-periodic function in the selected set of points on the basis of the values of that function in the same set of points. It allows to develop algebraic equations defining the steady state solution reached in a chosen point set for the nonlinear differential equations describing the AC machines when electrical and mechanical equations should be solved together. That set of those values allows determining the steady state solution at any time instant up to infinity. The algorithm described in this paper is competitive with respect to the one known in literature an approach based on the harmonic balance method operated in frequency domain.

The boundary layer on a fixed sphere on the axis of an unbounded rotating fluid

1982 ◽  
Vol 123 ◽  
pp. 219-236 ◽  
Author(s):  
S. C. R. Dennis ◽  
D. B. Ingham
Keyword(s):  
Boundary Layer ◽  
Steady State ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Procedure ◽  
Steady State Solution ◽  
State Solution ◽  
Partial Differential ◽  
Boundary Layer Equations ◽  
Finite Set

The problem of determining both the steady and unsteady axially symmetrical motion of a viscous incompressible fluid outside a fixed sphere when the fluid at large distances rotates as a solid body is considered. It is assumed that the Reynolds number for the motion is so large that the boundary-layer equations may be assumed to hold. The steady-state boundary-layer equations are solved using backward- forward differencing and the terminal solutions at the equator and the pole of the sphere are generatedas part ofthe numerical procedure. To check that this steady-state solution can be approached from an unsteady situation, the case of a sphere that is initially rotating with the same constant angular velocity as the fluid and is then impulsively brought to rest is investigated. I n this case the motion is governed by a coupled set of three nonlinear time-dependent partial differential equations, which are solved by employing the semi-analytical method of series truncation to reduce the number of independent variables by one and then solving by numerical methods a finite set of partial differential equations in one space variable and time. The physical properties of the flow are calculated as functions of the time and compared with the known solution at small times and the steady-state solution.

On the Squat of a Ship

1984 ◽  
Vol 28 (02) ◽  
pp. 107-117 ◽  
Author(s):  
P. M. Naghdi ◽  
M. B. Rubin
Keyword(s):  
Experimental Data ◽  
Steady State ◽  
Differential Equations ◽  
Froude Number ◽  
Steady State Solution ◽  
State Solution ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Sinkage And Trim

The problem of the squat of a "two-dimensional" ship is solved using a nonlinear steady-state solution of the differential equations of the theory of a directed fluid sheet. Particular attention is focused on the prediction of the sinkage and trim of the ship, and the results for a model ship qualitatively agree with available experimental data. Specifically, the solution presented here predicts the experimentally observed dependence of the sinkage and trim on the equilibrium depth of the water (regarded here as an incompressible, inviscid fluid), and predicts a nonzero drag for subcritical ship speeds (corresponding to the values of depth Froude number F < 1). The solution also exhibits certain detailed features of the sinkage curves which apparently were not observed in the experiments mentioned above. In this connection, additional relevant experiments are suggested.

Response of a Submerged Cylindrical Shell to an Axially Propagating Step Wave

1965 ◽  
Vol 32 (4) ◽  
pp. 788-792 ◽  
Author(s):  
M. J. Forrestal ◽  
G. Herrmann
Keyword(s):  
Cylindrical Shell ◽  
Steady State ◽  
Wave Front ◽  
Transverse Shear ◽  
Shell Theory ◽  
Steady State Solution ◽  
State Solution ◽  
Rotatory Inertia ◽  
Shear Deformations ◽  
Axial Coordinate

An infinitely long, circular, cylindrical shell is submerged in an acoustic medium and subjected to a plane, axially propagating step wave. The fluid-shell interaction is approximated by neglecting fluid motions in the axial direction, thereby assuming that cylindrical waves radiate away from the shell independently of the axial coordinate. Rotatory inertia and transverse shear deformations are included in the shell equations of motion, and a steady-state solution is obtained by combining the independent variables, time and the axial coordinate, through a transformation that measures the shell response from the advancing wave front. Results from the steady-state solution for the case of steel shells submerged in water are presented using both the Timoshenko-type shell theory and the bending shell theory. It is shown that previous solutions, which assumed plane waves radiated away from the vibrating shell, overestimated the dumping effect of the fluid, and that the inclusion of transverse shear deformations and rotatory inertia have an effect on the response ahead of the wave front.

scholarly journals Comparison of Solvers Performance for Load Flow Analysis

2019 ◽  
Vol 3 (1) ◽  
pp. 26 ◽  
Author(s):  
Vishnu Sidaarth Suresh
Keyword(s):  
Steady State ◽  
Power System ◽  
Reactive Power ◽  
Flow Analysis ◽  
Steady State Solution ◽  
Load Flow ◽  
State Solution ◽  
Computational Time ◽  
Load Flow Analysis ◽  
Active And Reactive Power

Load flow studies are carried out in order to find a steady state solution of a power system network. It is done to continuously monitor the system and decide upon future expansion of the system. The parameters of the system monitored are voltage magnitude, voltage angle, active and reactive power. This paper presents techniques used in order to obtain such parameters for a standard IEEE – 30 bus and IEEE-57 bus network and makes a comparison into the differences with regard to computational time and effectiveness of each solver

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