ANALYTICAL STUDY OF VIBRATIONAL RESONANCE IN AN OVERDAMPED BISTABLE OSCILLATOR

2008 ◽  
Vol 18 (06) ◽  
pp. 1767-1773 ◽  
Author(s):  
V. N. CHIZHEVSKY
Keyword(s):  
High Frequency ◽  
Analytical Study ◽  
Scaling Laws ◽  
Low Frequency ◽  
Approximate Solutions ◽  
Gain Factor ◽  
Bistable System ◽  
Vibrational Resonance ◽  
Periodic Signals ◽  
Good Agreement

The results of analytical study of vibrational resonance (VR) occurring in overdamped bistable system driven by two periodic signals with very different frequencies are presented. Approximate solutions for responses at the low-frequency as a function of the amplitude, and the frequency of the additional high frequency modulation which describe well the main features of vibrational resonance are obtained. Scaling laws for the gain factor and the switching threshold in VR are also found. Analytical results are compared with results of the numerical simulation, showing a good agreement.

Optimum Vibrational Resonance in a Time-Delay Bistable System Driven by Biharmonic Signals

2014 ◽  
Vol 651-653 ◽  
pp. 2172-2176
Author(s):  
Yun Liang Meng ◽  
Chang Xing Pei ◽  
Dong Wu Li
Keyword(s):  
Time Delay ◽  
High Frequency ◽  
Low Frequency ◽  
Signal Amplitude ◽  
Resonance Peak ◽  
Response Amplitude ◽  
Bistable System ◽  
Vibrational Resonance ◽  
Frequency Signal ◽  
High Frequency Signal

The optimum vibrational resonance in a time-delay bistable system driven by bihiarmonic signals is discussed in this paper. The theoretically expression for the response amplitude gain of low frequency signal in the time-delay bistable system is deduced, and the effects of time delay parameter on the optimum vibrational resonance peak and the required amplitude of high frequency signal are investigated. It is shown that the optimum vibrational resonance can be achieved by adjusting the high frequency signal amplitude and time delay parameter jointly. Meanwhile, the optimum vibrational resonance appeared periodically with time delay parameter and the period is equal to the period of low-frequency signal. The amplitude of high-frequency signal required for the optimum vibrational resonance can be fixed or varied with different time delay parameter depending on the ratio of the frequencies between biharmonic signals.

Non-uniform dependence on initial data for the generalized Degasperis–Procesi equation on the line

2016 ◽  
Vol 27 (03) ◽  
pp. 1650026
Author(s):  
Yanggeng Fu ◽  
Zanping Yu ◽  
Jianhe Shen
Keyword(s):  
Initial Data ◽  
Sobolev Spaces ◽  
High Frequency ◽  
Low Frequency ◽  
Approximate Solutions ◽  
Solution Map ◽  
High Frequency Part ◽  
Uniformly Continuous

In this paper, we show that the solution map of the generalized Degasperis–Procesi (gDP) equation is not uniformly continuous in Sobolev spaces [Formula: see text] for [Formula: see text]. Our proof is based on the estimates for the actual solutions and the approximate solutions, which consist of a low frequency and a high frequency part. It also exploits the fact that the gDP equation conserves a quantity which is equivalent to the [Formula: see text] norm.

scholarly journals Ferrite-Loaded Spidron Fractal Loop VHF Antenna for UAV Applications

2020 ◽  
Vol 10 (15) ◽  
pp. 5392 ◽  
Author(s):  
Won Bin Park ◽  
Young-Mi Park ◽  
Keum Cheol Hwang
Keyword(s):  
Frequency Band ◽  
High Frequency ◽  
Magnetic Loss ◽  
Low Frequency ◽  
Loop Antenna ◽  
High Frequency Band ◽  
Ferrite Material ◽  
Aerial Vehicle ◽  
Flat Ground ◽  
Good Agreement

In this letter, an electrically small Spidron fractal loop antenna operating in the VHF band is proposed. The ferrite material, which consists of a nickel-zinc combination, is loaded into inside of the loop antenna to increase the gain of the antenna in the low frequency band. To minimize the magnetic loss of the ferrite in the high frequency band, the amount and configuration of the ferrite are optimized using a genetic algorithm. Through this optimization step, the amount of the ferrite is decreased to 37.5% and the gain of the antenna in the high frequency band is improved. The size of the proposed antenna is 0.0242 × 0.0242 × 0.0051 λL3 at the lowest operating frequency. The proposed antenna was fabricated to verify the performance, and the simulated and measured results are in good agreement. The measured peak gains varied from −31.6 to −1.9 dBi within the measured frequency band. To examine the performance of the proposed antenna mounted on an unmanned aerial vehicle model (UAV), the antenna on a UAV was also simulated and the results were discussed. The simulated realized peak gains of the antenna on the UAV and on flat ground are similar.

Optimizing the Electrical Power in an Energy Harvesting System

2015 ◽  
Vol 25 (12) ◽  
pp. 1550171 ◽  
Author(s):  
Mattia Coccolo ◽  
Grzegorz Litak ◽  
Jesús M. Seoane ◽  
Miguel A. F. Sanjuán
Keyword(s):  
Energy Harvesting ◽  
Kinetic Energy ◽  
High Frequency ◽  
Energy Harvester ◽  
Electrical Power ◽  
Low Frequency ◽  
Electrical Energy ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Energy Harvesting System

In this paper, we study the vibrational resonance (VR) phenomenon as a useful mechanism for energy harvesting purposes. A system, driven by a low frequency and a high frequency forcing, can give birth to the vibrational resonance phenomenon, when the two forcing amplitudes resonate and a maximum in amplitude is reached. We apply this idea to a bistable oscillator that can convert environmental kinetic energy into electrical energy, that is, an energy harvester. Normally, the VR phenomenon is studied in terms of the forcing amplitudes or of the frequencies, that are not always easy to adjust and change. Here, we study the VR generated by tuning another parameter that is possible to manipulate when the forcing values depend on the environmental conditions. We have investigated the dependence of the maximum response due to the VR for small and large variations in the forcing amplitudes and frequencies. Besides, we have plotted color coded figures in the space of the two forcing amplitudes, in which it is possible to appreciate different patterns in the electrical power generated by the system. These patterns provide useful information on the forcing amplitudes in order to produce the optimal electrical power.

The origin of fluctuations and cross-field transport in idealized magnetic confinement systems

1981 ◽  
Vol 300 (1456) ◽  
pp. 547-557 ◽  
Keyword(s):  
Electric Fields ◽  
High Frequency ◽  
Scaling Laws ◽  
Scaling Law ◽  
Low Frequency ◽  
Magnetic Confinement ◽  
Upper Bounds ◽  
Transport Processes ◽  
General View ◽  
Long Wavelength

The study of plasma fluctuations and confinement in idealized systems such as octupoles and levitrons has contributed to the understanding of cross-field transport processes. The linear theory of plasma instabilities that cause fluctuations is well developed and can predict growth rates γ and wavelengths θ x around lines of force. However, the theoretical prediction of cross-field transport coefficient D ± is restricted to quasilinear estimates of upper bounds (for example, D = 1 2 γ λ x 2 ) because of the complexity of the full nonlinear calculation. Such quasilinear estimates usually far exceed the measured values and are of limited worth. A general view of the results from octupole and levitron experiments shows that under collisional conditions ( λ ei / L < 0 ) the diffusion coefficient, D , scales in the same way as classical collisional diffusion ( D α n / T e 1 2 B 2 ). Agreement is closely approached in many cases, sometimes even in the presence of fluctuations. Under collisionless conditions ( D α n / T e 1 2 B 2 ), Bohm diffusion scaling ( D α T e / B ) is found in the few cases where the scaling law has been determined. This behaviour is consistent with the general scaling laws of Connor & Taylor (1977) but is not understood in detail. In addition there is evidence, both experimental and theoretical, that long-wavelength low-frequency electric fields (convection cells) can be generated nonlinearly from high-frequency fluctuations and can contribute to cross-field transport

Vibrational resonance in a discrete neuronal model with time delay

2014 ◽  
Vol 28 (16) ◽  
pp. 1450103 ◽  
Author(s):  
Canjun Wang ◽  
Keli Yang ◽  
Shixian Qu
Keyword(s):  
Time Delay ◽  
Input Signal ◽  
High Frequency ◽  
Phase Synchronization ◽  
Low Frequency ◽  
Neuronal Model ◽  
Vibrational Resonance ◽  
Frequency Signal ◽  
High Frequency Signal ◽  
Neuron System

The effects of time delay on the vibrational resonance (VR) in a discrete neuron system with a low-frequency signal and a high-frequency signal are investigated by numerical simulations. The results show that there exists a delay time that optimizes the phase synchronization between the low-frequency input signal and the output signal. VR is induced by the time delay. Furthermore, the time delay can improve the response to a low-frequency input signal. Therefore, the time delay plays a constructive role in the transmission of a low-frequency signal by inducing and enhancing VR.

Experimental Evidence of Vibrational Resonance in a Mechanical Bistable Twin-Well Oscillator

2018 ◽  
Vol 13 (6) ◽  
Author(s):  
Abdrouf Abusoua ◽  
Mohammed F. Daqaq
Keyword(s):  
Experimental Evidence ◽  
High Frequency ◽  
Bistable System ◽  
Nonlinear Phenomenon ◽  
Resonant Response ◽  
Vibrational Resonance ◽  
Vibration Mitigation ◽  
Electrical Systems ◽  
High Frequency Excitation ◽  
Frequency Excitation

Vibrational resonance (VR) is a nonlinear phenomenon which occurs when a bistable system is subjected to a biharmonic excitation consisting of a small-amplitude resonant excitation and a large-amplitude high-frequency excitation. The result is that, under some conditions, the high-frequency excitation amplifies the resonant response associated with the slow dynamics. While VR was studied extensively in the open literature, most of the research studies used optical and electrical systems as platforms for experimental investigation. This paper provides experimental evidence that VR can also occur in a mechanical bistable twin-well oscillator and discusses the conditions under which VR is possible. The paper also demonstrates that the injection of the high frequency excitation can be used to change the effective stiffness of the slow response. This can be used for amplification/deamplification of the output signal which can be useful for sensitivity enhancement and/or vibration mitigation.

Enhancing the Weak Signal With Arbitrary High-Frequency by Vibrational Resonance in Fractional-Order Duffing Oscillators

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
J. H. Yang ◽  
Miguel A. F. Sanjuán ◽  
H. G. Liu
Keyword(s):  
Fractional Order ◽  
High Frequency ◽  
Low Frequency ◽  
Original System ◽  
Scale Transformation ◽  
Weak Signal ◽  
Vibrational Resonance ◽  
High Frequency Signal ◽  
System A ◽  
Auxiliary Signal

When the traditional vibrational resonance (VR) occurs in a nonlinear system, a weak character signal is enhanced by an appropriate high-frequency auxiliary signal. Here, for the harmonic character signal case, the frequency of the character signal is usually smaller than 1 rad/s. The frequency of the auxiliary signal is dozens of times of the frequency of the character signal. Moreover, in the real world, the characteristic information is usually indicated by a weak signal with a frequency in the range from several to thousands rad/s. For this case, the weak high-frequency signal cannot be enhanced by the traditional mechanism of VR, and as such, the application of VR in the engineering field could be restricted. In this work, by introducing a scale transformation, we transform high-frequency excitations in the original system to low-frequency excitations in a rescaled system. Then, we make VR to occur at the low frequency in the rescaled system, as usual. Meanwhile, the VR also occurs at the frequency of the character signal in the original system. As a result, the weak character signal with arbitrary high-frequency can be enhanced. To make the rescaled system in a general form, the VR is investigated in fractional-order Duffing oscillators. The form of the potential function, the fractional order, and the reduction scale are important factors for the strength of VR.

NONLINEAR INTERACTIONS BETWEEN TWO WIDELY SPACED MODES — EXTERNAL EXCITATION

1993 ◽  
Vol 03 (02) ◽  
pp. 417-427 ◽  
Author(s):  
S.A. NAYFEH ◽  
A.H. NAYFEH
Keyword(s):  
Natural Frequency ◽  
High Frequency ◽  
Analytical Study ◽  
Experimental Studies ◽  
Low Frequency ◽  
Harmonic Excitation ◽  
Frequency Mode ◽  
Large Contribution ◽  
High Frequency Mode ◽  
Two Degree Of Freedom

Recent experimental studies indicate that energy can be transferred from high- to low-frequency modes in structures with weak nonlinearity. In each of these experiments, a high-frequency mode was driven near its natural frequency but the response included a large contribution due to the first mode of the structure. In this paper, an analytical study of the response of a two-degree-of-freedom nonlinear system with widely spaced modes to a simple-harmonic excitation near the natural frequency of its high-frequency mode is presented. This system serves as a paradigm for the interaction of high- and low-frequency modes.

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