Excitation-Induced Stability in a Bistable Duffing Oscillator: Analysis and Experiments

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Z. Wu ◽  
R. L. Harne ◽  
K. W. Wang
Keyword(s):  
Perturbation Theory ◽  
Harmonic Balance ◽  
Duffing Oscillator ◽  
Excitation Level ◽  
Frequency Range ◽  
Numerical Studies ◽  
Method Of Harmonic Balance ◽  
Mathieu’S Equation ◽  
Excitation Conditions ◽  
Good Agreement

The excitation-induced stability (EIS) phenomenon in a harmonically excited bistable Duffing oscillator is studied in this paper. Criteria to predict system and excitation conditions necessary to maintain EIS are derived through a combination of the method of harmonic balance, perturbation theory, and stability theory for Mathieu's equation. Accuracy of the criteria is verified by analytical and numerical studies. We demonstrate that damping primarily determines the likelihood of attaining EIS response when several dynamics coexist while excitation level governs both the existence and frequency range of the EIS region, providing comprehensive guidance for realizing or avoiding EIS dynamics. Experimental results are in good agreement regarding the comprehensive influence of excitation conditions on the inducement of EIS.

scholarly journals Harmonic Balance-Based Approach for Quasi-Periodic Motions and Stability Analysis

2012 ◽  
Vol 134 (3) ◽  
Author(s):  
Mikhail Guskov ◽  
Fabrice Thouverez
Keyword(s):  
Harmonic Balance ◽  
Nonlinear Response ◽  
Duffing Oscillator ◽  
Point Of View ◽  
Periodic Motions ◽  
Computational Costs ◽  
Nonlinear Responses ◽  
Time Marching ◽  
The Stability ◽  
Good Agreement

Quasi-periodic motions and their stability are addressed from the point of view of different harmonic balance-based approaches. Two numerical methods are used: a generalized multidimensional version of harmonic balance and a modification of a classical solution by harmonic balance. The application to the case of a nonlinear response of a Duffing oscillator under a bi-periodic excitation has allowed a comparison of computational costs and stability evaluation results. The solutions issued from both methods are close to one another and time marching tests showing a good agreement with the harmonic balance results confirm these nonlinear responses. Besides the overall adequacy verification, the observation comparisons would underline the fact that while the 2D approach features better performance in resolution cost, the stability computation turns out to be of more interest to be conducted by the modified 1D approach.

scholarly journals A note on the method of harmonic balance

2001 ◽  
Vol 23 (1) ◽  
pp. 34-38
Author(s):  
Nguyen Van Dinh
Keyword(s):  
Asymptotic Method ◽  
Harmonic Balance ◽  
Free Oscillation ◽  
Duffing Oscillator ◽  
Oscillation Period ◽  
Small Oscillations ◽  
Method Of Harmonic Balance

Free oscillation period of the Duffing oscillator with cubic non-linearity was examined. A comparison between the exact period and those obtained by the asymptotic and the harmonic balance methods was done. It was shown that the remits given by the harmonic balance are acceptable even for large oscillations whereas the asymptotic method can only be applied for small oscillations.

The working standard of the unit of power of electromagnetic waves in the frequency range from 37,5 to 220 GHz

2020 ◽  
pp. 53-58
Author(s):  
A. V. Koudelny ◽  
I. M. Malay ◽  
V. A. Perepelkin ◽  
I. P. Chirkov
Keyword(s):  
Microwave Power ◽  
Electromagnetic Waves ◽  
Primary Standard ◽  
The State ◽  
Frequency Range ◽  
Working Standard ◽  
Extended Frequency Range ◽  
Effective Efficiency ◽  
Extended Frequency ◽  
Good Agreement

The possibility of using bolometric converters of microwave power from the State primary standard of the unit of power of electromagnetic waves in waveguide and coaxial paths GET 167-2017, which has a frequency range from 37,5 to 78,33 GHz, in an extended frequency range up to 220 GHz, is shown. Studies of semiconductor bolometric converters of microwave power in an extended frequency range have confirmed good agreement and smooth frequency characteristics of the effective efficiency factor of the converters. Based on the research results, the State working standard of the unit of power of electromagnetic waves of 0,1–10 mW in the frequency range from 37,5 to 220 GHz 3.1.ZZT.0288.2018 was approved. The technical characteristics of the working standard of the unit of power of electromagnetic oscillations in an extended frequency range from 37,5 to 220 GHz are given.

scholarly journals Functional analysis and the method of harmonic balance

1975 ◽  
Vol 32 (4) ◽  
pp. 457-464 ◽  
Author(s):  
C. A. Borges ◽  
L. Cesari ◽  
D. A. Sánchez
Keyword(s):  
Functional Analysis ◽  
Harmonic Balance ◽  
Method Of Harmonic Balance

Optical Vibration and Acceleration Sensor With a Silicon Cantilever

1999 ◽  
Author(s):  
Mitsuteru Kimura ◽  
Katsuhisa Toshima ◽  
Harunobu Satoh
Keyword(s):  
Simple Model ◽  
Optical Fiber ◽  
Resonance Frequency ◽  
Acceleration Sensor ◽  
Frequency Range ◽  
Silicon Cantilever ◽  
All Optical ◽  
New Type ◽  
Good Agreement ◽  
Optical Vibration

Abstract A new type all optical vibration and acceleration sensor using the combination of micromachined Si cantilever and optical fiber is proposed, and its fundamental characteristics are demonstrated. The light emitted from bulb-lens set into the V-groove is reflected at the reflector formed on the Si cantilever and then recoupled into the bulb-lens. Several sensors with different length (0.64–6.0 mm long) of the Si cantilever are fabricated to compare the theoretical resonance frequency fr obtained from the simple model and experimental ones. They had good agreement. From the sensing principle the sensing frequency range of the vibration is suitable below the fr of the Si cantilever of the sensor.

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