Determination of Parametric Resonances in Distributed Parameter Systems Using Frequency Analysis

2007 ◽  
Author(s):  
Yong-Kwan Lee ◽  
Leonid S. Chechurin
Keyword(s):  
Theoretical Analysis ◽  
Parametric Instability ◽  
Synchronous Generator ◽  
Constant Current ◽  
Time Varying ◽  
Digital Controllers ◽  
Stator Windings ◽  
Distributed Parameters ◽  
Time Varying Parameter ◽  
Parametric Resonances

Theoretical analysis of parametric instability for the control systems with distributed parameters shall be given. The approach to the solution of such systems can be composed of two parts, i.e. modeling and estimation of the distributed parameters and instability estimation of the periodical time-variant elements using parametric circumference. A control system with mechanical distributed parameters such as robot manipulators is introduced as an example. Theoretical analysis shows that the parametric instabilities occur by digital controllers or time-varying elements which excite the resonance regions of distributed parameters. An electro-mechanical transformer which consists of constant current motor and synchronous generator is applied as another example. Inductance between stator windings and rotor of the synchronous generator serves as a periodical time-varying parameter and long electrical line plays a role of an element with distributed parameters. Instability condition of the transformer rotation owing to the parametric resonance excitement was obtained.

Conditions of Parametric Resonance in Periodically Time-Variant Systems With Distributed Parameters

2009 ◽  
Vol 131 (3) ◽  
Author(s):  
Yong-Kwan Lee ◽  
Leonid S. Chechurin
Keyword(s):  
Parametric Resonance ◽  
Robot Manipulator ◽  
Synchronous Generator ◽  
Constant Current ◽  
Time Varying ◽  
Distributed Parameters ◽  
Time Varying Parameter ◽  
Manipulator Arm ◽  
The Stability ◽  
Systems With Distributed Parameters

Theoretical analysis of the stability problem for the control systems with distributed parameters shall be given. The approach to the analysis of such systems can be composed of two parts. First, the distributed parameter element is modeled by a frequency response function. Second, approximate conditions of parametric resonance are derived by a method of stationarization (describing functions of time-variant elements). The approach is illustrated by two examples. One is a robot-manipulator arm (distributed mechanical parameter system) controlled by a controller with a modulator/demodulator cascade (time-varying element). Another is an electromechanical transformer that consists of a constant current motor and a synchronous generator. Inductance between stator windings and the rotor of the synchronous generator serves as a periodical time-varying parameter, and a long electrical line plays the role of an element with distributed parameters. In both examples, dangerous (in terms of the first parametric resonance) regions for time-varying parameter are obtained theoretically and compared with simulation experiment.

Influence of Axial Excitations and of Boundary Conditions on the Parametric Instability of a Beam

1995 ◽  
Author(s):  
Régis Dufour ◽  
Alain Berlioz ◽  
Thomas Streule
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Time Varying ◽  
Periodic Force ◽  
Modal Reduction ◽  
Time Varying Parameter ◽  
The Stability

Abstract In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It shows that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

The Establishment of Time-Varying Parameter Model of the Synchronous Generator Loss of Field

2014 ◽  
Vol 672-674 ◽  
pp. 1238-1243
Author(s):  
Yan Ling Lv ◽  
Hong Zhe Bai ◽  
Wen Hai Chen ◽  
Chong Teng
Keyword(s):  
Simulation Analysis ◽  
Synchronous Generator ◽  
Time Varying ◽  
Mathematical Operation ◽  
First Order ◽  
Leakage Field ◽  
Asynchronous Operation ◽  
Verification Methods ◽  
Time Varying Parameter ◽  
Damper Windings

When synchronous generator operates steadily, the slip remains essentially unchanged, and the traditional first-order mathematical model can be used to analyze its operating procedures. But when it occurs asynchronously failure, the traditional model of a first-order mathematical operation can no longer be used accurately to analyze its state. This paper establishes time-varying parameter model considering the rotor eddy based on mutual leakage field winding and straight shaft damper windings resistance, and uses simulation analysis and comparison of experimental verification methods to verify the correctness of the model for synchronous generator asynchronous operation, which provides a theoretical basis.

Parametric Instability of a Beam Due to Axial Excitations and to Boundary Conditions

1998 ◽  
Vol 120 (2) ◽  
pp. 461-467 ◽  
Author(s):  
R. Dufour ◽  
A. Berlioz
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
Ritz Method ◽  
Parametric Instability ◽  
Experimental Tests ◽  
Time Varying ◽  
Periodic Force ◽  
Modal Reduction ◽  
Time Varying Parameter ◽  
The Stability

In this paper the stability of the lateral dynamic behavior of a pinned-pinned, clamped-pinned and clamped-clamped beam under axial periodic force or torque is studied. The time-varying parameter equations are derived using the Rayleigh-Ritz method. The stability analysis of the solution is based on Floquet’s theory and investigated in detail. The Rayleigh-Ritz results are compared to those of a finite element modal reduction. It is shown that the lateral instabilities of the beam depend on the forcing frequency, the type of excitation and the boundary conditions. Several experimental tests enable the validation of the numerical results.

scholarly journals Experimental Investigation of Vibration Response of a Flexible Coupler In a Four Bar Mechanism Due to Varying Crank Length and Crank Speed

2018 ◽  
Vol 248 ◽  
pp. 01008 ◽  
Author(s):  
Rizky Arman ◽  
Andi Isra Mahyuddin ◽  
Wenny Marthiana ◽  
Iman Satria
Keyword(s):  
Dynamic Behaviour ◽  
Parametric Instability ◽  
Excitation Frequency ◽  
Vibration Response ◽  
Time Varying ◽  
Dynamic Parameters ◽  
Inertial Effects ◽  
Time Varying Parameter ◽  
Increase Productivity ◽  
Crank Length

Effort to increase productivity calls for increasingly higher operating speed. Consequently, many part of a machinery are made as light as possible to avoid the detrimental inertial effects. This condition means several of the elements are no longer rigid and tend to experience elastic deformation in operation. The existence of the deformation yields element possessing position dependent dynamic parameters. Mechanisms with time-varying parameter have a phenomenon known as parametric instability where the mechanism could becomes dynamically unstable at several frequency bands, even at relatively low excitation frequency. This research investigates the dynamic behaviour of a flexible coupler on an experimental four-bar mechanism setup. The study examines the coupler vibration response due to varying crank length and crank speed.

ANTICIPATED FUTURE CONSUMPTION IN AN ENDOGENOUS GROWTH MODEL

2020 ◽  
pp. 1-37
Author(s):  
Manuel A. Gómez ◽  
Goncalo Monteiro
Keyword(s):  
Theoretical Analysis ◽  
Endogenous Growth ◽  
Growth Model ◽  
Reference Point ◽  
Time Varying ◽  
Standard Specification ◽  
Equilibrium Dynamics ◽  
Current Consumption ◽  
Endogenous Growth Model ◽  
Future Consumption

We devise an endogenous growth model in which agents’ utility depends not only on current consumption but also on the pleasure of anticipated future consumption. We consider the case in which agents derive satisfaction from their own anticipatory feelings—inward-looking or internal anticipation—and the case in which agents derive utility from anticipation of other people’s future consumption—outward-looking or external anticipation. We characterize the effects of introducing a forward-looking consumption reference on the dynamics of the economy. Whereas the inward-looking economy features transitional dynamics, the outward-looking economy does not. The distortions caused by the externality in the economy with external habits can be corrected by subsidizing income at a time-varying rate or by means of a tax on consumption at a decreasing rate. We contrast the equilibrium dynamics of our specification to the more standard specification of the habit formation consumption reference point. Numerical simulations supplement the theoretical analysis.

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