A SIMPLIFIED CIRCUIT OF THE SEISMIC ELECTRIC METHOD AND ITS STEADY‐STATE SOLUTION

Geophysics ◽  
1936 ◽  
Vol 1 (3) ◽  
pp. 336-339 ◽  
Author(s):  
M. M. Slotnick
Keyword(s):  
Steady State ◽  
Steady State Solution ◽  
State Solution ◽  
Successive Approximations ◽  
Method Of Successive Approximations ◽  
Steady State Response ◽  
State Response ◽  
In Series ◽  
The One ◽  
Electric Effect

The Seismic Electric Effect gives rise to the problem of finding the steady state response of a circuit consisting of an inductance and a response of a circuit consisting of an inductance and a resistance of the form R+A cos cot (R>A) in series with a D.C. input. In this paper a solution is given, other than the one usually obtained by the method of successive approximations.

Closed-Form, Steady-State Solution for the Unbalance Response of a Rigid Rotor in Squeeze Film Damper

1983 ◽  
Vol 105 (3) ◽  
pp. 551-556 ◽  
Author(s):  
D. L. Taylor ◽  
B. R. K. Kumar
Keyword(s):  
Steady State ◽  
Closed Form ◽  
Closed Form Solution ◽  
Steady State Solution ◽  
State Solution ◽  
Squeeze Film ◽  
Steady State Response ◽  
Rigid Rotor ◽  
Squeeze Film Damper ◽  
State Response

This paper considers the steady-state response due to unbalance of a planar rigid rotor carried in a short squeeze film damper with linear centering spring. The damper fluid forces are determined from the short bearing, cavitated (π film) solution of Reynold’s equation. Assuming a circular centered orbit, a change of coordinates yields equations whose steady-state response are constant eccentricity and phase angle. Focusing on this steady-state solution results in reducing the problem to solutions of two simultaneous algebraic equations. A method for finding the closed-form solution is presented. The system is nondimensionalized, yielding response in terms of an unbalance parameter, a damper parameter, and a speed parameter. Several families of eccentricity-speed curves are presented. Additionally, transmissibility and power consumption solutions are present.

The Steady-State Response of the Double Bilinear Hysteretic Model

1965 ◽  
Vol 32 (4) ◽  
pp. 921-925 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Steady State ◽  
Nonlinear Systems ◽  
Steady State Solution ◽  
Degree Of Freedom ◽  
State Solution ◽  
Steady State Response ◽  
Hysteretic Model ◽  
Jump Phenomenon ◽  
State Response ◽  
The Stability

The steady-state response of a one-degree-of-freedom double bilinear hysteretic model is investigated and it is shown that this model gives rise to the jump phenomenon which is associated with certain nonlinear systems. The stability of the steady-state solution is discussed and it is shown that the model predicts an unbounded resonance for finite excitation.

An Efficient Algorithm for Computing the Steady-State Dynamic Response of High-Speed Mechanisms

1994 ◽  
Author(s):  
Tyler J. Selstad ◽  
Kambiz Farhang
Keyword(s):  
Steady State ◽  
High Speed ◽  
Steady State Solution ◽  
Time Varying ◽  
Initial Condition ◽  
Steady State Response ◽  
Periodicity Condition ◽  
Varying Coefficients ◽  
State Response ◽  
Time Varying Coefficients

Abstract An efficient method for obtaining the steady-state response of linear systems with periodically time varying coefficients is developed. The steady-state solution is obtained by dividing the fundamental period into a number of intervals and establishing, based on a fourth-order Rung-Kutta formulation, the relation between the response at the start and end of the period. Imposition of periodicity condition upon the response facilitates computation of the initial condition that yields the steady-state values in a single pass; i.e. integration over only one period. Through a practical example, the method is shown to be more accurate and computationally more efficient than other known methods for computing the steady-state response.

The Timoshenko Beam on an Elastic Foundation and Subject to a Moving Step Load, Part 1: Steady-State Response

1996 ◽  
Vol 118 (3) ◽  
pp. 277-284 ◽  
Author(s):  
S. F. Felszeghy
Keyword(s):  
Steady State ◽  
Boundary Conditions ◽  
Elastic Foundation ◽  
Timoshenko Beam ◽  
Equations Of Motion ◽  
Steady State Solution ◽  
State Solution ◽  
Actual Problem ◽  
State Response ◽  
Particular Solution

The response of a simply supported semi-infinite Timoshenko beam on an elastic foundation to a moving step load is determined. The response is found from summing the solutions to two mutually complementary sets of governing equations. The first solution is a particular solution to the forced equations of motion. The second solution is a solution to a set of homogeneous equations of motion and nonhomogeneous boundary conditions so formulated as to satisfy the initial and boundary conditions of the actual problem when the two solutions are summed. As a particular solution, the steady-state solution is used which is the motion that would appear stationary to an observer traveling with the load. Steady-state solutions are developed in Part 1 of this article for all load speeds greater than zero. It is shown that a steady-state solution which is identically zero ahead of the load front exists at every load speed, in the sense of generalized functions, including the critical speeds when the load travels at the minimum phase velocity of propagating harmonic waves and the sonic speeds. The solution to the homogeneous equations of motion is developed in Part 2 where the two solutions in question are summed and numerical results are presented as well.

On Efficient Computation of the Steady-State Response of Linear Systems With Periodic Coefficients

1996 ◽  
Vol 118 (3) ◽  
pp. 522-526 ◽  
Author(s):  
T. J. Selstad ◽  
K. Farhang
Keyword(s):  
Steady State ◽  
Linear Systems ◽  
Steady State Solution ◽  
Time Varying ◽  
Steady State Response ◽  
Efficient Computation ◽  
Periodicity Condition ◽  
Varying Coefficients ◽  
State Response ◽  
Time Varying Coefficients

An efficient method for obtaining the steady-state response of linear systems with periodically time varying coefficients is developed. The steady-state solution is obtained by dividing the fundamental period into a number of intervals and establishing, based on a fourth-order Rung-Kutta formulation, the relation between the response at the start and end of the period. Imposition of periodicity condition upon the response facilitates computation of the initial condition that yields the steady-state values in a single pass; i.e., integration over only one period. Through a practical example, the method is shown to be more accurate and computationally more efficient than other known methods for computing the steady-state response.

Effects of Static Friction on the Forced Response of Frictionally Damped Turbine Blades

1984 ◽  
Vol 106 (1) ◽  
pp. 65-69 ◽  
Author(s):  
A. Sinha ◽  
J. H. Griffin
Keyword(s):  
Steady State ◽  
Turbine Blades ◽  
Time Integration ◽  
Ground Vibration ◽  
Static Friction ◽  
Steady State Solution ◽  
Forced Response ◽  
Steady State Response ◽  
Integration Algorithm ◽  
State Response

The effect of static friction on the design of flexible blade-to-ground vibration dampers used in gas turbine engines is investigated. It is found that for γ (ratio of dynamic and static friction coefficients) less than 1, the steady-state response is essentially harmonic when the damper slip load, S, is small. However, as S increases beyond a certain value, the steady-state response ceases to be simply harmonic and, while still periodic, is a more complex waveform. The transition slip load is found to be lower for smaller γ. The maximum possible reduction in vibratory stresses increases as γ decreases. These analytical results are compared with those from the conventional numerical time integration method. In addition, an efficient time integration algorithm is described which can be used to predict the peak displacements of the transition solution without tracing the whole waveform, a useful procedure when no harmonic steady-state solution exists. The conditions under which blade response can be adequately modeled by simulating only dynamic friction are established.

scholarly journals Computationally Efficient Modeling of DC-DC Converters for PV Applications

Energies ◽  
2020 ◽  
Vol 13 (19) ◽  
pp. 5100
Author(s):  
Fabio Corti ◽  
Antonino Laudani ◽  
Gabriele Maria Lozito ◽  
Alberto Reatti
Keyword(s):  
Steady State ◽  
Simulation System ◽  
Photovoltaic Device ◽  
Steady State Response ◽  
Computationally Efficient ◽  
Computational Costs ◽  
State Response ◽  
State Detection ◽  
Space Formulation ◽  
The One

In this work, a computationally efficient approach for the simulation of a DC-DC converter connected to a photovoltaic device is proposed. The methodology is based on a combination of a highly efficient formulation of the one-diode model for photovoltaic (PV) devices and a state-space formulation of the converter as well as an accurate steady-state detection methodology. The approach was experimentally validated to assess its accuracy. The model is accurate both in its dynamic response (tested in full linearity and with a simulated PV device as the input) and in its steady-state response (tested with an outdoor experimental measurement setup). The model detects automatically the reaching of a steady state, thus resulting in lowered computational costs. The approach is presented as a mathematical model that can be efficiently included in a large simulation system or statistical analysis.

Radiation Fin Efficiency for One-Dimensional Heat Flow in a Circular Fin

1959 ◽  
Vol 81 (4) ◽  
pp. 327-329 ◽  
Author(s):  
R. L. Chambers ◽  
E. V. Somers
Keyword(s):  
Steady State ◽  
Heat Flow ◽  
Thermal Power ◽  
Steady State Solution ◽  
State Solution ◽  
Design Parameters ◽  
One Dimensional ◽  
Fin Efficiency ◽  
Annular Fin ◽  
The One

The one-dimensional steady-state solution for radiation from one side of an annular fin has been computed for values of the two design parameters 0⩽ϵσθi3Kro-ri⩽2.0 and 1.001⩽ρ=rori⩽15.0. The solution supplies design information needed for satellite thermal-power dissipating surfaces.

Asymptotic behaviour of solutions of the hydrodynamic model of semiconductors

2002 ◽  
Vol 132 (2) ◽  
pp. 359-378 ◽  
Author(s):  
Hailiang Li ◽  
Peter Markowich ◽  
Ming Mei
Keyword(s):  
Steady State ◽  
Asymptotic Behaviour ◽  
Small Perturbation ◽  
Hydrodynamic Model ◽  
Existence And Uniqueness ◽  
Steady State Solution ◽  
State Solution ◽  
Energy Estimates ◽  
One Dimensional ◽  
The One

Degond and Markowich discussed the existence and uniqueness of a steady-state solution in the subsonic case for the one-dimensional hydrodynamic model of semiconductors. In the present paper, we reconsider the existence and uniqueness of a globally smooth subsonic steady-state solution, and prove its stability for small perturbation. The proof method we adopt in this paper is based on elementary energy estimates.

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