Shaopu Yang

Nonlinear dynamical analysis and parameters optimization of four semi-active on-off dynamic vibration absorbers

In this paper the averaging method is used to research the approximately analytical solution of a semi-active on-off dynamic vibration absorber (DVA). At first the approximately analytical solutions for the two existing semi-active on-off DVAs, named as velocity-velocity based ground-hook control and displacement- velocity based ground-hook control, are established by the averaging method. Then two other new semi-active on-off DVAs, named as velocity-displacement based ground-hook control and displacement-displacement based ground-hook control, are presented for the first time in this paper and also researched analytically. Moreover, all the optimal parameters of the four semi-active DVAs, including the stiffness and the maximum and minimum damping ratio of the subsystem, are optimized to make the peak of the displacement transmissibility curve minimum, based on the amplitude-frequency equations from approximately analytical solutions. The comparisons of the displacement transmissibility obtained from the approximate solutions and the numerical ones are fulfilled, and the results certify that the approximate solutions have satisfactory precision. At last, the statistical results of the stochastic responses of the primary systems, including the original single degree-of-freedom system, the optimally passive DVA system, and the four semi-active on-off DVA systems, are obtained when subject to random excitation. The results show that the two new semi-active DVAs presented in this paper are almost as excellent as the existing two semi-active DVAs, and all of the four semi-active DVAs have better control performance than the optimally passive DVA.

Analysis of an Isolation System with Magnetorheological Damper

The paper aims at studying a single-degree-of-freedom isolation system with a magnetorheological (MR) fluid damper under harmonic excitations. MR dampers exhibit hysteretic behavior when subjected to sinusoidal loads, and the systems with MR dampers are of strong nonlinear dynamical behaviors. A concise model of MR damper is introduced to describe the hysteretic behavior. Assuming that the steady state motion of the system is periodic and symmetric, and connecting two subintervals together analytically to construct an entire cycle of the period motion, a closed analytical solution is obtained. From the solution, the hysteretic critical displacement of the steady state motion of the isolation system, the hysteretic critical velocity, the maximum amplitude, and their time lags could be computed. For a special case, the solution is reduced to the classic results of Den Hartog on the forced vibrations with coulomb friction. The results of this study are helpful for understanding the characteristics of MR dampers to provide effective damping for the purpose of vibration isolation or suppression.

An Electro-Mechanical Coupling Model of Magnetorheological Damper

Magnetorheological (MR) dampers are a class of semi-active control devices with field-dependent property. To achieve the desirable performance of the controlled system with damper, the fundamental issue is to establish a proper model. In this paper, a novel modeling idea considering the damper and control device as one system is put forward. Based on this idea, a mathematical representation for characterizing an electro-mechanical coupling model of MR damper is presented, where the rate-dependent hysteretic relation of the damping forces vs. velocity and electromagnetic hysteresis is well demonstrated. Then a simulation model, SIMULINK, is set up. Comparison between the predicted and the experimental results indicates that the model is satisfactory for reproducing the dynamic behaviors of MR damper.

Subharmonic Resonance of Van Der Pol Oscillator with Fractional-Order Derivative

The subharmonic resonance of van der Pol (VDP) oscillator with fractional-order derivative is studied by the averaging method. At first, the first-order approximate solutions are obtained by the averaging method. Then the definitions of equivalent linear damping coefficient (ELDC) and equivalent linear stiffness coefficient (ELSC) for subharmonic resonance are established, and the effects of the fractional-order parameters on the ELDC, the ELSC, and the dynamical characteristics of system are also analysed. Moreover, the amplitude-frequency equation and phase-frequency equation of steady-state solution for subharmonic resonance are established. The corresponding stability condition is presented based on Lyapunov theory, and the existence condition for subharmonic resonance (ECSR) is also obtained. At last, the comparisons of the fractional-order and the traditional integer-order VDP oscillator are fulfilled by the numerical simulation. The effects of the parameters in fractional-order derivative on the steady-state amplitude, the amplitude-frequency curves, and the system stability are also studied.

Analytical research on a single degree-of-freedom semi-active oscillator with time delay

In this paper a single degree-of-freedom semi-active oscillator with time delay is researched. By averaging method, the first-order approximately analytical solution is obtained, and the stability condition is also established based on the Lyapunov theory. The analytical results show that the amplitude and the stability condition of the steady-state solution are all periodic functions of time delay, with the same period as the excitation one. Moreover, another simple case, namely the semi-active oscillator without time delay, is also investigated based on the first-order approximately analytical solution, and the result shows that the steady-state solution in this case is unconditionally stable. The comparisons of the analytical solution and the numerical one are fulfilled, and the results verify the correctness and satisfactory precision of the first-order approximately analytical solution. At last, the selection or design of an appropriate time delay to improve control performance through the first-order approximately analytical solution is studied.

Parameters Optimization for a Kind of Dynamic Vibration Absorber with Negative Stiffness

A new type of dynamic vibration absorber (DVA) with negative stiffness is studied in detail. At first, the analytical solution of the system is obtained based on the established differential motion equation. Three fixed points are found in the amplitude-frequency curves of the primary system. The design formulae for the optimum tuning ratio and optimum stiffness ratio of DVA are obtained by adjusting the three fixed points to the same height according to the fixed-point theory. Then, the optimum damping ratio is formulated by minimizing the maximum value of the amplitude-frequency curves according to optimization principle. According to the characteristics of negative stiffness element, the optimum negative stiffness ratio is also established and it could still keep the system stable. In the end, the comparison between the analytical and the numerical solutions verifies the correctness of the analytical solution. The comparisons with three other traditional DVAs under the harmonic and random excitations show that the presented DVA performs better in vibration absorption. This result could provide theoretical basis for optimum parameters design of similar DVAs.

Dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation

In this paper, the computation schemes for periodic solutions of the forced fractional-order Mathieu-Duffing equation are derived based on incremental harmonic balance (IHB) method. The general forms of periodic solutions are founded by the IHB method, which could be useful to obtain the periodic solutions with higher precision. The comparisons of the approximate analytical solutions by the IHB method and numerical integration are fulfilled, and the results certify the correctness and higher precision of the solutions by the IHB method. The dynamical analysis of strongly nonlinear fractional-order Mathieu-Duffing equation is investigated by the IHB method. Then, the effects of the excitation frequency, fractional order, fractional coefficient, and nonlinear stiffness coefficient on the complex dynamical behaviors are analyzed. At last, the detailed results are summarized and the conclusions are made, which present some useful information to analyze and/or control the dynamical response of this kind of system.

Application of Magnetorheological Damper in Vibration Control of Locomotive

The simplified dynamical equations for hunting motion of locomotive are firstly established. Then the dynamical behavior of the semi-active suspension of the locomotive with magnetorheological (MR) damper is investigated, where the MR model is obtained based on experimental results. In order to compare the performance of the semi-active suspension with MR damper, the passive control suspension, the semi-active on-off control suspension and the active suspension are also discussed. The simulation results show that the semi-active suspension of the locomotive with MR damper could lower the vibration of locomotive effectively almost as the active control. Based on the control strategy presented here, not only the angular acceleration of the locomotive body could be lowered, which reduces the possibility of hunting motion, but also the yaw angles of the frontal and back bogies would be lowered, which improves the security of operation

Effect of interpolation methods on fast computation of fractional Fourier transform

This paper makes the fast computation method of fractional Fourier transform (FrFT) by Ozaktas more perfect. The different effect of two interpolation methods, including spline interpolation and Shannon interpolation, on the fast computation of FrFT is investigated. The results show that Shannon interpolation method has a better performance and is preferable to other interpolation methods, which makes the fast computation of FrFT more elegant and is useful for application in many fields.

Dynamical Analysis on Single Degree-of-Freedom Semiactive Control System by Using Fractional-Order Derivative

The single degree-of-freedom (SDOF) system under the control of three semiactive methods is analytically studied in this paper, where a fractional-order derivative is used in the mathematical model. The three semiactive control methods are on-off control, limited relative displacement (LRD) control, and relative control, respectively. The averaging method is adopted to provide an analytical study on the performance of the three different control methods. Based on the comparison between the analytical solutions with the numerical ones, it could be proved that the analytical solutions are accurate enough. The effects of the fractional-order parameters on the control performance, especially the relative and absolute displacement transmissibility, are analyzed. The research results indicate that the steady-state amplitudes of the three semiactive systems with fractional-order derivative in the model could be significantly reduced and the control performance can be greatly improved.