Useful Details about Testing Protective Relays with Signals that Include Effects of Travelling Waves

The dynamic behavior of an autocatalytic reaction with a product inhibition term is studied in a flow system. A unique steady state exists in the continuous tank reactor. Linear stability analysis predicts either a stable node, a focus or an unstable saddle-focus. Sustained oscillations around the unstable focus can occur for high values of the Damköhler number (Da). In the distributed system, travelling, standing or complex oscillatory waves are detected. For a low value of Da, travelling waves with a pseudo-constant pattern are observed. With an intermediate value of Da, single or multiple standing waves are obtained. The temporal behavior indicates also the appearance of retriggering or echo waves. For a high value of Da, both single peak and complex multipeak oscillations are found. In the cell model, both regular oscillations near the inlet and chaotic behavior downstream are observed. In the dispersion model, higher Peclet numbers (Pe) eliminate the oscillations. The spatial profile shows a train of pulsating waves for the discrete model and a single pulsating or solitary wave for the continuous model.

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Calculating the response of waveguides to base excitation using the wave and finite element method

Journal of Vibration and Control ◽

10.1177/1077546320981315 ◽

2021 ◽

pp. 107754632098131

Author(s):

Jamil Renno ◽

Sadok Sassi ◽

Wael I Alnahhal

Keyword(s):

Finite Element Method ◽

Finite Element ◽

Transfer Functions ◽

Travelling Waves ◽

Model Free ◽

Time Harmonic ◽

Element Approach ◽

Response Transfer ◽

Free Wave Propagation ◽

Element Method

The prediction of the response of waveguides to time-harmonic base excitations has many applications in mechanical, aerospace and civil engineering. The response to base excitations can be obtained analytically for simple waveguides only. For general waveguides, the response to time-harmonic base excitations can be obtained using the finite element method. In this study, we present a wave and finite element approach to calculate the response of waveguides to time-harmonic base excitations. The wave and finite element method is used to model free wave propagation in the waveguide, and these characteristics are then used to find the amplitude of excited waves in the waveguide. Reflection matrices at the boundaries of the waveguide are then used to find the amplitude of the travelling waves in the waveguide and subsequently the response of the waveguide. This includes the displacement and stress frequency response transfer functions. Numerical examples are presented to demonstrate the approach and to discuss the numerical efficiency of the proposed method.

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Impact of the purposeful kinesis on travelling waves

Physica A Statistical Mechanics and its Applications ◽

10.1016/j.physa.2021.125821 ◽

2021 ◽

Vol 571 ◽

pp. 125821

Author(s):

Nurdan Çabukoǧlu

Keyword(s):

Travelling Waves

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