Stochastic Resonance in Strongly Coupled Duffing and Van der pol Oscillators Under Trichotomous Noise and Bearing Fault Diagnosis

2019 ◽  
Vol 19 (03) ◽  
pp. 2050023
Author(s):  
Gang Zhang ◽  
Xia Wu ◽  
Tianqi Zhang
Keyword(s):  
Stochastic Resonance ◽  
Coupling Coefficient ◽  
Damping Coefficient ◽  
System Response ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
Strongly Coupled ◽  
Force Coupling ◽  
Trichotomous Noise

Weak signal detection is an important topic, which has been widely studied in various fields. Different from other signal processing methods, stochastic resonance (SR) can utilize noise to enhance the characteristic frequency. Inspired by the unique advantage of SR, the strongly coupled Duffing and Van der pol SR system (SCD-VSR) is investigated. The simulation results show that the relationship between the output average signal–noise ratio increase (MSNRI) and different jump values of trichotomous noise presents different odd symmetrical distribution. It is also found that a double SR phenomenon could be observed when the damping coefficient of Van der pol system is small. Moreover, as the damping coefficient of the Duffing system increases, the output response would become gradually smooth. In addition,a smaller damping force coupling coefficient combined with a large restoring force coupling coefficient would achieve better system response. In the case of detecting an analog signal, MSNRI of SCD-VSR is larger than that of both classical bistable SR system (CBSR) and coupled Duffing SR system (CDSR). In addition, the experiments suggest that SCD-VSR could obtain a higher MSNRI and better detection effect, which implies the performance is superior to CBSR and CDSR.

scholarly journals Stochastic P-bifurcation in a bistable Van der Pol oscillator with fractional time-delay feedback under Gaussian white noise excitation

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Yajie Li ◽  
Zhiqiang Wu ◽  
Guoqi Zhang ◽  
Feng Wang ◽  
Yuancen Wang
Keyword(s):  
Time Delay ◽  
White Noise ◽  
Gaussian White Noise ◽  
Singularity Theory ◽  
Van Der Pol Oscillator ◽  
Order System ◽  
Damping Force ◽  
Van Der Pol ◽  
Restoring Force ◽  
White Noise Excitation

Abstract The stochastic P-bifurcation behavior of a bistable Van der Pol system with fractional time-delay feedback under Gaussian white noise excitation is studied. Firstly, based on the minimal mean square error principle, the fractional derivative term is found to be equivalent to the linear combination of damping force and restoring force, and the original system is further simplified to an equivalent integer order system. Secondly, the stationary Probability Density Function (PDF) of system amplitude is obtained by stochastic averaging, and the critical parametric conditions for stochastic P-bifurcation of system amplitude are determined according to the singularity theory. Finally, the types of stationary PDF curves of system amplitude are qualitatively analyzed by choosing the corresponding parameters in each area divided by the transition set curves. The consistency between the analytical solutions and Monte Carlo simulation results verifies the theoretical analysis in this paper.

A Study of the Roll Motion by Means of a Free Decay Test

2010 ◽  
Vol 132 (3) ◽  
Author(s):  
Hamid Zeraatgar ◽  
Mohsen Asghari ◽  
Firooz Bakhtiari-Nejad
Keyword(s):  
Damping Ratio ◽  
Nonlinear Damping ◽  
Damping Coefficient ◽  
Roll Motion ◽  
Damping Force ◽  
Restoring Force ◽  
Cubic Form ◽  
Damping Coefficients ◽  
Decay Test ◽  
Nonlinear Form

In this study, a method for the extraction of damping by tracing free roll decay is presented. For this purpose, in calm waters, a bulk carrier model is given a large initial roll angle and then released. Consequently, the roll motion is recorded. Restoring coefficients and virtual moments of inertia for the model are determined by means of an inclining test and recording the damped period, respectively. The linear damping coefficient is evaluated by using the damping ratio. Four different forms of combinations of restoring moment and damping coefficient are assumed in order to determine the nonlinear form of the roll motion. These equations are numerically solved for various damping coefficients and results are compared with the experimental data. By virtue of this comparison, the damping coefficients are determined for each case. It may be concluded that the use of the nonlinear restoring moment, which is an odd polynomial of the fifth order, and the cubic form for the nonlinear damping moment best fits the roll behavior for the ship model. The amount of energy dissipated by the damping moments is also calculated in the time domain. The energy method also confirms that the nonlinear form of restoring force in conjunction with the cubic form of the damping force is the best solution of the roll motion for small to large angles.

Parametric Study of Damping Characteristics of Magneto-Rheological Damper: Mathematical and Experimental Approach

2020 ◽  
Vol 15 (3) ◽  
pp. 37-48
Author(s):  
Zubair Rashid Wani ◽  
Manzoor Ahmad Tantray
Keyword(s):  
Structural Control ◽  
Research Work ◽  
Testing Machine ◽  
Input Voltage ◽  
Damping Coefficient ◽  
Control Technique ◽  
Damping Force ◽  
Active Devices ◽  
Active Structural Control ◽  
Magneto Rheological

The present research work is a part of a project was a semi-active structural control technique using magneto-rheological damper has to be performed. Magneto-rheological dampers are an innovative class of semi-active devices that mesh well with the demands and constraints of seismic applications; this includes having very low power requirements and adaptability. A small stroke magneto-rheological damper was mathematically simulated and experimentally tested. The damper was subjected to periodic excitations of different amplitudes and frequencies at varying voltage. The damper was mathematically modeled using parametric Modified Bouc-Wen model of magneto-rheological damper in MATLAB/SIMULINK and the parameters of the model were set as per the prototype available. The variation of mechanical properties of magneto-rheological damper like damping coefficient and damping force with a change in amplitude, frequency and voltage were experimentally verified on INSTRON 8800 testing machine. It was observed that damping force produced by the damper depended on the frequency as well, in addition to the input voltage and amplitude of the excitation. While the damping coefficient (c) is independent of the frequency of excitation it varies with the amplitude of excitation and input voltage. The variation of the damping coefficient with amplitude and input voltage is linear and quadratic respectively. More ever the mathematical model simulated in MATLAB was in agreement with the experimental results obtained.

Application of Semi-Active Oil Damper System to Base Isolation Systems

2002 ◽  
Author(s):  
Takashi Kawai ◽  
Yasuo Tsuyuki ◽  
Yutaka Inoue ◽  
Osamu Takahashi ◽  
Koji Oka
Keyword(s):  
Base Isolation ◽  
Shaking Table ◽  
The Other ◽  
Damping Coefficient ◽  
Damping Force ◽  
Mass Model ◽  
Maximum Acceleration ◽  
Rubber Bearing ◽  
Single Mass ◽  
Isolation Systems

This paper deals with one of the applications of the Semi-Active Oil Damper system, which applies base isolation systems reducing the maximum acceleration. The theory of the Semi-Active Oil Damper system is based on Karnopp Theory. The theory has been actually now in use for a Semi-active suspension system of the latest Shinkansen (New trunk lines) trains to improve passenger’s comfortable riding. Various experiments have been conducted using a single mass model whose weight is 15 ton on the shaking table. This model is supported by the rubber bearing. The natural frequency is 0.33Hz of this system. Two Semi-Active Oil Damper were installed in the model and excited the table for one horizontal direction. The maximum damping force of each Semi-Active Oil Damper used for the model is 4.21 kN. The damper can change the damping coefficient by utilizing two solenoid valves. Therefore, the dynamic characteristic of the damping force has two modes. One is a hard damping coefficient and the other is a soft one. It was confirmed that the maximum acceleration of the Semi-Active Oil Damper system can be reduced more than 20% in comparison with the passive Oil Damper system in our tests.

Stochastic resonance for a fractional oscillator with random trichotomous mass and random trichotomous frequency

2017 ◽  
Vol 31 (30) ◽  
pp. 1750231 ◽  
Author(s):  
Lifeng Lin ◽  
Huiqi Wang ◽  
Suchuan Zhong
Keyword(s):  
Stochastic Resonance ◽  
Exact Expression ◽  
Order Moment ◽  
Periodic Signal ◽  
Transformation Technique ◽  
First Order ◽  
Fractional Oscillator ◽  
Trichotomous Noise ◽  
Output Amplitude ◽  
Fractional System

The stochastic resonance (SR) phenomena of a linear fractional oscillator with random trichotomous mass and random trichotomous frequency are investigate in this paper. By using the Shapiro–Loginov formula and the Laplace transformation technique, the exact expression of the first-order moment of the system’s steady response is derived. The numerical results demonstrate that the evolution of the output amplitude is nonmonotonic with frequency of the periodic signal, noise parameters and fractional order. The generalized SR (GSR) phenomena, including single GSR (SGSR) and doubly GSR (DGSR), and trebly GSR (TGSR), are detected in this fractional system. Then, the GSR regions in the [Formula: see text] plane are determined through numerical calculations. In addition, the interaction effect of the multiplicative trichotomous noise and memory can diversify the stochastic multiresonance (SMR) phenomena, and induce reverse-resonance phenomena.

An Impedance-Based Approach for Rods With Shear-Type Damping Layer Treatment

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
P. W. Wang ◽  
D. Q. Zhuang
Keyword(s):  
High Frequency ◽  
Continuous Model ◽  
Damping Coefficient ◽  
System Response ◽  
Traditional Model ◽  
Constrained Layer Damping ◽  
High Frequency Range ◽  
Frequency Range ◽  
Shear Type ◽  
Shear Spring

An impedance-based approach for analyzing an axial rod with shear-type damping layer treatment is proposed. The rod and shear-type damping layer are regarded as two subsystems and both impedances are calculated analytically. The system impedance can be obtained through the impedance coupling between the host rod and the damping layer. The shear-type damping layer is regarded as a shear spring with complex shear modulus. Under the traditional model, the damping coefficient diminishes with the increasing frequency. The paper develops two shear-type damping layer models, including the single degree-of-freedom (SDOF) model and continuous model to predict the behavior of the damping layer. Both damping layer models are compared with the traditional model and the system responses from these models are validated by finite element method (FEM) code COMSOL Multiphysics. Results show that the damping coefficients of both the traditional shear-spring model and SDOF model diminish as the increasing frequency so that the system responses are discrepant with that from COMSOL in the high frequency range. On the other hand, the system response from the continuous model is consistent with that from COMSOL in the full frequency range. Hence, the continuous damping layer model can predict a correct damping coefficient in the high frequency range and this property can be also employed to improve the analysis of the constrained-layer damping treated structures. Finally, the modal loss factor and fundamental frequency of the system with respect to different damping layer thicknesses are presented using the developed approach.

Dynamic Property Analysis of Damping Rubber in Rail Fastenings under Different Deformation Condition

2014 ◽  
Vol 494-495 ◽  
pp. 706-710
Author(s):  
Bin Zhang ◽  
Yan Yun Luo ◽  
Zhi Nan Shi
Keyword(s):  
Mechanical Model ◽  
Dynamic Stiffness ◽  
Excitation Frequency ◽  
Nonlinear Damping ◽  
Deformation Condition ◽  
Damping Force ◽  
Restoring Force ◽  
Dynamic Mechanical ◽  
Large Distortion ◽  
Hydraulic Servo

This paper studies the experimental research on dynamic characteristics of the damping rubber in high elastic fastening by the electro-hydraulic servo movement tester. Based on a hypothesis superposition theory of nonlinear elastic restoring force and nonlinear damping force, a non-linear dynamic mechanical model is proposed. The dynamic stiffness and damping parameters of the rubber are obtained in different deformation conditions based on the dynamic mechanical model. The dynamic stiffness is analyzed, and the results show that dynamic stiffness is closely related to excitation frequency and amplitude. Furthermore the dynamic stiffness is analyzed under different free surface of rubber components by using FEM. That also reveals the changeable characteristics and affected factors of the damping rubber of the high elastic fastenings in large distortion condition.

Galerkin Scheme-Based Determination of Survival Probability of Oscillators With Fractional Derivative Elements

2016 ◽  
Vol 83 (12) ◽  
Author(s):  
Pol D. Spanos ◽  
Alberto Di Matteo ◽  
Yezeng Cheng ◽  
Antonina Pirrotta ◽  
Jie Li
Keyword(s):  
Fractional Derivative ◽  
Survival Probability ◽  
Stochastic Averaging ◽  
Kolmogorov Equation ◽  
System Response ◽  
Statistical Linearization ◽  
Van Der Pol ◽  
Galerkin Scheme ◽  
Confluent Hypergeometric Functions

In this paper, an approximate semi-analytical approach is developed for determining the first-passage probability of randomly excited linear and lightly nonlinear oscillators endowed with fractional derivative elements. The amplitude of the system response is modeled as one-dimensional Markovian process by employing a combination of the stochastic averaging and the statistical linearization techniques. This leads to a backward Kolmogorov equation which governs the evolution of the survival probability of the oscillator. Next, an approximate solution of this equation is sought by resorting to a Galerkin scheme. Specifically, a convenient set of confluent hypergeometric functions, related to the corresponding linear oscillator with integer-order derivatives, is used as orthogonal basis for this scheme. Applications to the standard viscous linear and to nonlinear (Van der Pol and Duffing) oscillators are presented. Comparisons with pertinent Monte Carlo simulations demonstrate the reliability of the proposed approximate analytical solution.

scholarly journals Design of a Novel Magnetorheological Damper Adaptable to Low and High Stroke Velocity of Vehicle Suspension System

2020 ◽  
Vol 10 (16) ◽  
pp. 5586
Author(s):  
Bo-Gyu Kim ◽  
Dal-Seong Yoon ◽  
Gi-Woo Kim ◽  
Seung-Bok Choi ◽  
Aditya Suryadi Tan ◽  
...  
Keyword(s):  
Shape Function ◽  
Mr Damper ◽  
Effective Area ◽  
Magnetorheological Damper ◽  
Damping Coefficient ◽  
Vehicle Suspension ◽  
Damping Force ◽  
Piston Velocity ◽  
Suspension Systems ◽  
Vehicle Suspension System

In this study, a new class of magnetorheological (MR) damper, which can realize desired damping force at both low and high speeds of vehicle suspension systems, is proposed and its salient characteristics are shown through computer simulations. Unlike conventional MR dampers, the proposed MR damper has a specific pole shape function and therefore the damping coefficient is changed by varying the effective area of the main orifice. In addition, by controlling the opening or closing the bypass orifice, the drastic change of the damping coefficient is realizable. After briefly describing the operating principle, a mathematical modeling is performed considering the pole shape function which is a key feature of the proposed MR damper. Then, the field-dependent damping force and piston velocity-dependent characteristics are presented followed by an example on how to achieve desired damping force characteristics by changing the damping coefficient and slope breaking point which represents the bilinear damping property.

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