Vibrational Resonance in an Overdamped System with a Fractional Order Potential Nonlinearity

2018 ◽  
Vol 28 (07) ◽  
pp. 1850082 ◽  
Author(s):  
Jianhua Yang ◽  
Dawen Huang ◽  
Miguel A. F. Sanjuán ◽  
Houguang Liu
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Low Frequency ◽  
Response Amplitude ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Frequency Excitation ◽  
Overdamped System

We investigate the vibrational resonance by the numerical simulation and theoretical analysis in an overdamped system with fractional order potential nonlinearities. The nonlinearity is a fractional power function with deflection, in which the response amplitude presents vibrational resonance phenomenon for any value of the fractional exponent. The response amplitude of vibrational resonance at low-frequency is deduced by the method of direct separation of slow and fast motions. The results derived from the theoretical analysis are in good agreement with those of numerical simulation. The response amplitude decreases with the increase of the fractional exponent for weak excitations. The amplitude of the high-frequency excitation can induce the vibrational resonance to achieve the optimal response amplitude. For the overdamped systems, the nonlinearity is the crucial and necessary condition to induce vibrational resonance. The response amplitude in the nonlinear system is usually not larger than that in the corresponding linear system. Hence, the nonlinearity is not a sufficient factor to amplify the response to the low-frequency excitation. Furthermore, the resonance may be also induced by only a single excitation acting on the nonlinear system. The theoretical analysis further proves the correctness of the numerical simulation. The results might be valuable in weak signal processing.

Control of amplitude death by coupling range in a network of fractional-order oscillators

2020 ◽  
Vol 34 (31) ◽  
pp. 2050303
Author(s):  
Rui Xiao ◽  
Zhongkui Sun
Keyword(s):  
Theoretical Analysis ◽  
Numerical Simulations ◽  
Fractional Order ◽  
Coupling Strength ◽  
Low Frequency ◽  
System Size ◽  
Coupled Systems ◽  
Amplitude Death ◽  
Function Relationship ◽  
The Relationship

We investigate the oscillating dynamics in a ring of network of nonlocally delay-coupled fractional-order Stuart-Landau oscillators. It is concluded that with the increasing of coupling range, the structures of death islands go from richness to simplistic, nevertheless, the area of amplitude death (AD) state is expanded along coupling delay and coupling strength directions. The increased coupling range can prompt the coupled systems with low frequency to occur AD. When system size varies, the area of death islands changes periodically, and the linear function relationship between periodic length and coupling range can be deduced. Thus, one can modulate the oscillating dynamics by adjusting the relationship between coupling range and system size. Furthermore, the results of numerical simulations are consistent with theoretical analysis.

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 Acoustic Behaviors of Dual Layered Nonwoven Absorbers: From Model Building to Experiment Verification

2014 ◽  
Vol 22 (02) ◽  
pp. 1450001
Author(s):  
Jianli Liu ◽  
Xinjin Liu ◽  
Wei Bao ◽  
Shuangshan Wang ◽  
Longmin Chen ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Sound Absorption ◽  
Model Building ◽  
Low Frequency ◽  
Physical Structure ◽  
Absorption Model ◽  
Absorption Coefficients ◽  
Experiment Verification ◽  
The Impact

Nonwovens are ideal materials for use as noise control elements because of their unique physical structure and special acoustic behaviors, especially when their structures are complicatedly designed. In this paper, we first deduce a sound absorption model for dual-layered porous nonwovens by extending the Zwikker and Kosten theory. Then a theoretical analysis and a numerical simulation of the impact of thickness and porosity of outer and inner layers on the sound absorption coefficient are followed by an experiment designed to compare the calculated sound absorption coefficients and the measured ones. Experiment results indicate that the measured and the calculated sound absorption coefficients are very similar in trend with change of thickness, porosity and sound frequency, apart from the obvious difference at low frequency. Finally, the main reasons for the differences between the theoretic data and the experimental ones are also explored.

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.

scholarly journals NUMERICAL INVESTIGATION OF SIGNAL AMPLIFICATION VIA VIBRATIONAL RESONANCE IN CHUA'S CIRCUIT

2020 ◽  
Vol 6 ◽  
pp. 14
Author(s):  
John Abidemi Laoye ◽  
Taiwo Olakunle Roy-Layinde ◽  
Kehinde Adam Omoteso ◽  
Rasaki Kola Odunaike
Keyword(s):  
Low Frequency ◽  
Response Amplitude ◽  
Chua’S Circuit ◽  
Response Curves ◽  
Vibrational Resonance ◽  
Periodic Force ◽  
Chua's Circuit ◽  
Chua’S Oscillator ◽  
Conductance Parameter ◽  
Cubic Polynomial

In this paper, we numerically investigated the occurrence of Vibrational Resonance in a modified Chua's oscillator with a smooth nonlinearity, described by a cubic polynomial. Response curves generated from the numerical simulation at the low frequency reveal that the system's response amplitude could be controlled by modulating the conductance parameter of the Chua's circuit, rather modulating the parameters of the fast-periodic force. Modulating the frequency of the fast-periodic force slightly reduces the response amplitude; shifts the peak point to a higher value of the amplitude of the fast-periodic force by widening the resonance curves. Within certain parameter regime of the high frequency (Ω >100ω), the system's response gets saturated, and further increase does not affect its amplitude.

scholarly journals Vibrational Resonance and Electrical Activity Behavior of a Fractional-Order FitzHugh–Nagumo Neuron System

Mathematics ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 87
Author(s):  
Jia-Wei Mao ◽  
Dong-Liang Hu
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Neuron Model ◽  
Low Frequency ◽  
Order Model ◽  
Vibrational Resonance ◽  
Frequency Signal ◽  
Neuron System ◽  
Order Neuron ◽  
Activity Behavior

Making use of the numerical simulation method, the phenomenon of vibrational resonance and electrical activity behavior of a fractional-order FitzHugh–Nagumo neuron system excited by two-frequency periodic signals are investigated. Based on the definition and properties of the Caputo fractional derivative, the fractional L1 algorithm is applied to numerically simulate the phenomenon of vibrational resonance in the neuron system. Compared with the integer-order neuron model, the fractional-order neuron model can relax the requirement for the amplitude of the high-frequency signal and induce the phenomenon of vibrational resonance by selecting the appropriate fractional exponent. By introducing the time-delay feedback, it can be found that the vibrational resonance will occur with periods in the fractional-order neuron system, i.e., the amplitude of the low-frequency response periodically changes with the time-delay feedback. The weak low-frequency signal in the system can be significantly enhanced by selecting the appropriate time-delay parameter and the fractional exponent. In addition, the original integer-order model is extended to the fractional-order model, and the neuron system will exhibit rich dynamical behaviors, which provide a broader understanding of the neuron system.

scholarly journals Effect of Modulated Signals on Vibrational Resonance in a Harmonically Trapped Potential System

2021 ◽  
Vol 13 (3) ◽  
pp. 797-807
Author(s):  
B. Bhuvaneshwari ◽  
S. V. Priyatharsini ◽  
V. Chinnathambi ◽  
S. Rajasekar
Keyword(s):  
Low Frequency ◽  
Response Amplitude ◽  
External Signal ◽  
Amplitude Curve ◽  
Vibrational Resonance ◽  
Potential Wells ◽  
Fm Signals ◽  
Potential System ◽  
Single Well ◽  
Modulated Signals

We consider a harmonically trapped potential system driven by modulated signals with two widely different frequencies ω and Ω, where Ω >> ω. The forms of modulated signals are amplitude modulated (AM) and frequency-modulated (FM) signals. An amplitude-modulated external signal is consisting of a low-frequency (ω) component and two high-frequencies (Ω + ω) and (Ω − ω) whereas the frequency modulated signal consisting of the frequency components such as f sinωt cos(g cosΩt) and f sin(g cosΩt) cosωt. Depending upon the values of the parameters in the potential function, an odd number of potential wells of different depths can be generated. We numerically investigate the effect of these modulated signals on vibrational resonance (VR) in single-well, three-well, five-well and seven-well potentials. Different from traditional VR theory in the present paper, the enhancement of VR is made by the amplitudes of the AM and FM signals. We show the enhanced response amplitude (Q) at the low-frequency ω, showing the greater number of resonance peaks and non-decay response amplitude on the response amplitude curve due to the modulated signals in all the potential wells. Furthermore, the response amplitude of the system driven by the AM signal exhibits hysteresis and a jump phenomenon. Such behavior of Q is not observed in the system driven by the FM signal.

Nonplanar Motion of a String due to Two-Frequency Excitation

2001 ◽  
Author(s):  
Kimihiko Yasuda ◽  
Keisuke Kamiya
Keyword(s):  
Numerical Simulation ◽  
Theoretical Analysis ◽  
Perturbation Method ◽  
Natural Frequencies ◽  
Multiple Scales ◽  
Method Of Multiple Scales ◽  
Harmonic Excitation ◽  
Chaotic Motions ◽  
Frequency Excitation

Abstract It is known that, under certain conditions, a stretched string subjected to a planar harmonic excitation executes nonplanar motions due to the instability of the palanar motion. In recent years, studies on bifurcations of such nonplanar motions to amplitude modulated quasiperiodic motions and chaotic motions have been reported. However no literatures on the problem of nonplanar motions due to a multi-frequency excitation are found. In this paper, the possibility of nonplanar motions in a string due to a two-frequency excitation is studied. For this purpose two cases are considered, i.e. one in which both components of the excitation are in a plane, and one in which they are perpendicular to each other. In both cases the sum of the frequencies of the components is supposed to near to twice one of the natural frequencies of the string. Theoretical analysis using the perturbation method of multiple scales and numerical simulation are carried out to show that nonplanar motions occur.

Vibrational Resonance in a Fractional Order Quintic Oscillator System with Time Delay Feedback

2020 ◽  
Vol 30 (02) ◽  
pp. 2050025 ◽  
Author(s):  
Wen Guo ◽  
Lijuan Ning
Keyword(s):  
Time Delay ◽  
Fractional Order ◽  
Bifurcation Point ◽  
Low Frequency ◽  
Approximate Expression ◽  
Vibrational Resonance ◽  
Point Change ◽  
Oscillator System ◽  
Single Well ◽  
System With Time Delay

Vibrational resonance is studied in a fractional order quintic oscillator system with delayed feedback. By utilizing the perturbation theory, the theoretical approximate expression of the response amplitude at low-frequency is obtained. In the presence of fractional order and time delay, resonance phenomena are studied in the single-well, double-well and triple-well potentials, respectively. Meanwhile, the good agreement between theoretical prediction and numerical simulation verifies the validity of theoretical analysis. It is found that by altering the fractional order derivative, the occurrence of new resonances is more frequent. As delay increases, the bifurcation point and the equilibrium point change periodically. In addition, fractional order, time delay feedback and high-frequency force amplitude can be appropriately selected to achieve the goal of maximizing the output in different systems. In particular, an intersection that affects the triple-well potential bifurcation point was found.

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.

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