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.

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.

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.

Methods for Determinning Critical Values of Nonconservative Loads in Problems of Stability of Mechanical Systems

2019 ◽  
pp. 3-13 ◽  
Author(s):  
V.P. Radin ◽  
V.P. Chirkov ◽  
A.V. Shchugorev ◽  
V.N. Shchugorev
Keyword(s):  
Complex Function ◽  
Mechanical Systems ◽  
Critical Values ◽  
The Finite Element Method ◽  
Natural Oscillations ◽  
Flowing Liquid ◽  
Stability Problems ◽  
Distributed Parameters ◽  
The Stability ◽  
Systems With Distributed Parameters

Methods for determining critical values of nonconservative loads in stability problems of mechanical systems with distributed parameters are considered in this work. Based on a dynamic approach to stability problems, the method of direct integration of the linearized equation of perturbed motion is proposed, and the problem of determining critical loads is reduced to the problem of minimizing a complex function of several variables. As a second method, the method of decomposition of the solution of the equation of perturbed motion in the forms of natural oscillations is presented. The fundamentals of the application of the finite element method to the problems of stability under the action of non-conservative loads are also described. The methods are illustrated on classical problems: the stability of the cantilever rod under the action of potential and tracking forces and the stability of the pipeline section with flowing liquid. The accuracy and convergence of the latter two methods are analyzed depending on the number of members in the series and the number of finite elements.

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.

Sign in / Sign up

Export Citation Format

Share Document