An inverse model of MR damper using optimal neural network and system identification

Magnetorheological (MR) damper is one of the more promising new devices for vibration control of structures. External energy required by the adjustable fluid damper is minuscule while speed of its response is in the order of milliseconds. The MR damper is a semi-active control device and has been characterized by a set of non-linear differential equations which represent a forward model of the MR damper, i.e., the model can generate a force to a given displacement and applied voltage.This paper presents an inverse model of the MR damper, i.e., the model can predict the required voltage so that the MR damper can produce the desired force for the requirement of vibration control of structures. The inverse model has been constructed by using a multi-layer perceptron optimal neural network and system identification, which are Gauss-Newton-based Levenberg-Marquardt training algorithm, optimal brain surgeon strategy and autoregressive with exogenous variables (ARX) model. Based on the data from numerical simulation of the MR damper, the trained optimal neural networks can accurately predict voltage. If the inverse model is used in a control system, the semi-active vibration control can be implemented easily by using the semi-active MR damper.     

起落架磁流变减摆器模糊PID控制算法的研究

为了减小飞机机轮的摆振,提高飞机乘坐的舒适性和驾驶的安全性,将磁流变控制技术应用于飞机起落架减摆器,实现减摆器阻尼力的实时智能控制。针对磁流变减摆器,建立了飞机起落架摆振的半主动控制非线性动力学模型,设计了模糊PID控制算法,并使用Matlab/Simulink建立了半主动控制仿真模型。通过调节流过磁感线圈的电流大小改变磁流变减摆器的阻尼力,从而减小机轮摆动实现半主动控制。通过动力学仿真,在给定速度下分别对比未安装减摆器、被动控制下以及半主动控制下机轮摆角、侧向位移、侧滑角随时间变化的曲线,结果表明了模糊PID控制算法的正确性和可行性,该控制策略可以较好的抑制机轮的摆振,同时也表明模糊PID控制算法具有良好的可控性,减摆效果也明显优于传统的被动控制。     

A comparison of two nonlinear damping mechanisms in a vibration isolator

The vibration transmissibility characteristics of a single-degree-of-freedom (SDOF) passive vibration isolation system with different nonlinear dampers are investigated in this paper. In one configuration, the damper is assumed to be linear and viscous, and is connected to the mass so that it is perpendicular to the spring (horizontal damper). The vibration is in the direction of the spring. The second configuration is one in which the damper is in parallel with the spring but the damping force is proportional to the cube of the relative velocity across the damper (cubic damping). Both configurations are studied for small amplitudes of excitation, when some analysis can be conducted based on analytical expressions, and for large amplitudes of excitation, where the analysis is based on numerical simulations. It is found that the two nonlinear systems can outperform the linear system when force transmissibility is considered. However, for displacement transmissibility, the system with the horizontal damper exhibits some desirable properties, but the system with cubic damping does not.     

Autoparametric vibration absorber effect to reduce the first symmetric mode vibration of a curved beam/panel

This paper presents the implementation of autoparametric phenomena to reduce the symmetrical vibration of a curved beam/panel under external harmonic excitation. The internal energy transfer of a first symmetric mode into first anti-symmetric mode in a curved panel is one example of autoparametric vibration absorber effect. This is similar to the vibration energy transfer from the resonance of a primary structure to the resonance of a secondary spring–mass (tuned mass damper). The nonlinear response of a curved beam is analyzed using an equation with two modes, and a shaker test. The effect of different configurations of the curve beam/panel, including damping ratios and excitation levels, on the energy transfer of the first symmetric mode to the first anti-symmetric mode was studied.The conventional tuned mass damper (TMD) can reduce the resonance response by energy transfer using damping dissipation, whereas an autoparametric vibration absorber (AVA) can reduce the resonance response by energy transfer using parametric interaction. The results indicate that there is a non-absorption region in which vibration is amplified. For the AVA, the non-absorption region can be minimized by tuning the resonance frequency of the first anti-symmetric mode to half of the first symmetric mode resonance frequency using additional mass. No additional damping material is required for achieving sufficient vibration reduction. The AVA can maintain reliable performance in hot and corrosive environments where damping material cannot perform effectively. This paper presents the first successful experimental results of an autoparametric vibration absorption mechanism in a curved beam.     

磁流变液阻尼器在转子振动控制中的应用

设计了一种转子振动控制用的剪切式磁流变液阻尼器,建立了磁流变液阻尼器－悬臂转子系统的分析模型,理论和实验研究了转子系统的不平衡响应特性。研究表明,随着施加磁场强度的增加,磁流变液阻尼和刚度增大,转子系统的临界振幅明显下降,系统的临界转速也明显提高。通过简单的开关控制,可抑止转子通过临界转速过程中的振动。     

H-infinity optimization of a variant design of the dynamic vibration absorber—Revisited and new results

The H_∞ optimum parameters of a dynamic vibration absorber (DVA) with ground-support are derived to minimize the resonant vibration amplitude of a single degree-of-freedom (sdof) system under harmonic force excitation. The optimum parameters which are derived based on the classical fixed-points theory and reported in literature for this non-traditional DVA are shown to be not leading to the minimum resonant vibration amplitude of the controlled mass. A new procedure is proposed for the H_∞ optimization of such a dynamic vibration absorber. A new set of optimum tuning frequency and damping of the absorber is derived, thereby resulting in lower maximum amplitude responses than those reported in the literature. The proposed optimized variant DVA is also compared to a ground-hooked damper of the same damping capacity of the damper in the DVA. It is proved that the proposed optimized DVA has better suppression of the resonant vibration amplitude of the controlled system than both the traditional DVA and also the ground-hooked damper if the proposed design procedure of the variant DVA is followed.     

EFFECT OF SEATING ON EXPOSURES TO WHOLE-BODY VIBRATION IN VEHICLES

The vibration isolation efficiency of seating has been evaluated in 100 work vehicles in 14 categories (cars, vans, lift trucks, lorries, tractors, buses, dumpers, excavators, helicopters, armoured vehicles, mobile cranes, grass rollers, mowers and milk floats). Seat isolation efficiency, expressed by the SEAT value, was determined for all seats (67 conventional seats and 33 suspension seats) from the vertical acceleration measured on the floors and on the seats of the vehicles.For most categories of vehicle, the average SEAT value was less than 100%, indicating that the average seat provided some attenuation of vibration. However, there were large variations in SEAT values between vehicles within categories. Two alternative vibration frequency weightings (W_b from BS 6841, 1987; W_k from ISO 2631, 1997) yielded SEAT values that differed by less than 6%. Overall, the SEAT values determined by two alternative methods (the ratio of r.m.s. values and the ratio of vibration dose values) differed by less than 4·5% when using weighting W_b, although larger differences may be expected in some situations. The median SEAT value for the suspension seats was 84·6%; the median SEAT value for the conventional seats was 86·9% (based on weighting W_b and the ratio of r.m.s. values).Predicted SEAT values were obtained assuming that each seat could be interchanged between vehicles without altering its transmissibility. The calculations suggest that 94% of the vehicles investigated might benefit from changing the current seat to a seat from one of the other vehicles investigated. Although the predictions are based on assumptions that will not always apply, it is concluded that the severity of whole-body vibration exposures in many work environments can be lessened by improvements to seating dynamics.     

Development of a new damper to reduce resonant vibrations in lightweight steel joist floors

Floor vibrations annoying to humans often occur in lightweight constructions. A number of methods to solve the problem of resonant vibrations are reported in the literature. Tuned mass damper, semi-active tuned vibration absorber and active control system are all examples of existing methods. A new method has been tested in laboratory environment on a prefabricated floor containing a resilient ceiling with a size up to 6.8×4.8 m². The method takes advantage of small pieces of visco-elastic material connected between the ceiling joists and the primary beams. A finite element model is used to calculate the correct amount of visco-elastic material. The new damper is especially effective in damping mode shapes where the ceiling oscillates out of phase relative to the floor but shows improvements for other mode shapes as well.     

EFFECT OF MUSCLE TENSION ON NON-LINEARITIES IN THE APPARENT MASSES OF SEATED SUBJECTS EXPOSED TO VERTICAL WHOLE-BODY VIBRATION

In subjects exposed to whole-body vibration, the cause of non-linear dynamic characteristics with changes in vibration magnitude is not understood. The effect of muscle tension on the non-linearity in apparent mass has been investigated in this study. Eight seated male subjects were exposed to random and sinusoidal vertical vibration at five magnitudes (0·35-1·4 m/s² r.m.s.). The random vibration was presented for 60 s over the frequency range 2·0-20 Hz; the sinusoidal vibration was presented for 10 s at five frequencies (3·15, 4·0, 5·0, 6·3 and 8·0 Hz). Three sitting conditions were adopted such that, in two conditions, muscle tension in the buttocks and the abdomen was controlled. It was assumed that, in these two conditions, involuntary changes in muscle tension would be minimized. The force and acceleration at the seat surface were used to obtain apparent masses of subjects. With both sinusoidal and random vibration, there was statistical support for the hypothesis that non-linear characteristics were less clear when muscle tension in the buttocks and the abdomen was controlled. With increases in the magnitude of random vibration from 0·35 to 1·4 m/s² r.m.s., the apparent mass resonance frequency decreased from 5·25 to 4·25 Hz with normal muscle tension, from 5·0 to 4·38 Hz with the buttocks muscles tensed, and from 5·13 to 4·5 Hz with the abdominal muscles tensed. Involuntary changes in muscle tension during whole-body vibration may be partly responsible for non-linear biodynamic responses.     

Hysteresis-induced bifurcation and chaos in a magneto-rheological suspension system under external excitation

The magneto-rheological damper(MRD) is a promising device used in vehicle semi-active suspension systems, for its continuous adjustable damping output. However, the innate nonlinear hysteresis characteristic of MRD may cause the nonlinear behaviors. In this work, a two-degree-of-freedom(2-DOF) MR suspension system was established first, by employing the modified Bouc–Wen force–velocity(F –v) hysteretic model. The nonlinear dynamic response of the system was investigated under the external excitation of single-frequency harmonic and bandwidth-limited stochastic road surface.The largest Lyapunov exponent(LLE) was used to detect the chaotic area of the frequency and amplitude of harmonic excitation, and the bifurcation diagrams, time histories, phase portraits, and power spectrum density(PSD) diagrams were used to reveal the dynamic evolution process in detail. Moreover, the LLE and Kolmogorov entropy(K entropy) were used to identify whether the system response was random or chaotic under stochastic road surface. The results demonstrated that the complex dynamical behaviors occur under different external excitation conditions. The oscillating mechanism of alternating periodic oscillations, quasi-periodic oscillations, and chaotic oscillations was observed in detail. The chaotic regions revealed that chaotic motions may appear in conditions of mid-low frequency and large amplitude, as well as small amplitude and all frequency. The obtained parameter regions where the chaotic motions may appear are useful for design of structural parameters of the vibration isolation, and the optimization of control strategy for MR suspension system.     

Quasi-active suspension design using magnetorheological dampers

Quasi-active damping is a method of coupled mechanical and control system design using multiple semi-active dampers. By designing the systems such that the desired control force may always be achieved using a combination of the dampers, quasi-active damping seeks to approach levels of vibration isolation achievable through active damping, whilst retaining the desirable attributes of semi-active systems. In this article a design is proposed for a quasi-active, base-isolating suspension system.Control laws are firstly defined in a generalised form, where semi-active dampers are considered as idealised variable viscous dampers. This system is used to demonstrate in detail the principles of quasi-active damping, in particular the necessary interaction between mechanical and control systems. It is shown how such a system can produce a tunable, quasi-active region in the frequency response of very low displacement transmissibility.Quasi-active control laws are then proposed which are specific for use with magnetorheological dampers. These are validated in simulation using a realistic model of the damper dynamics, again producing a quasi-active region in the frequency response. Finally, the robustness of the magnetorheological, quasi-active suspension system is demonstrated.     

Energy harvesting using semi-active control

This paper presents the application of semi-active control for optimising the power harvested by an electro-mechanical energy harvester. A time-periodic damper, defined by a Fourier series, is introduced for energy harvesting in order to increase the performance of the device. An analytical solution for the transmissibility and the average absorbed power is derived based on the method of harmonic balance. The coefficients of the semi-active model are optimised to maximise the harvested power. The harvested power from the optimum periodic time-varying damper at a particular frequency is compared and is shown to be greater than that from an optimum passive damper and a semi-active on–off damper not only at that particular frequency but also at other frequencies. In addition, the performance of the optimised periodic time-varying damper is also compared with an arbitrary semi-active time-periodic damper, which has the same transmissibility at resonance. An optimisation is carried out to maximise the power in a frequency range and the optimum damper is derived as a function of the excitation frequency. The numerical results are validated with the analytical approach.     

Application of dynamic vibration absorbers in floating raft system

To improve the isolation performance of the traditional floating raft system, dynamic vibration absorber (DVA) is introduced into floating raft in this research. The mathematical models of floating raft system consisting of beams are implemented by assembling the mobility matrices of the subsystems. Then the power flow transmission characteristics of the coupled system with/without the DVAs are investigated to evaluate the vibration reduction performance of DVAs. Numerical simulations are performed to explore the influence of several parameters, such as the setting positions, damping and mass of the passive DVAs, on the vibration reduction effects of DVAs. Moreover the vibration reduction performance of the semi-active absorber adjusting its stiffness adaptively is analyzed for the case of time-varying frequency excitation. In addition, the vibration reduction effects of semi-active DVAs under multi-frequency excitation are investigated. The results show that DVAs can significantly improve the isolation performance of floating raft system.     

Studies of the performance of particle dampers under dynamic loads

This paper presents a systematic investigation of the performance of particle dampers (vertical and horizontal) attached to a primary system (single-degree-of-freedom (SDOF) and multi-degree-of-freedom (MDOF)) under different dynamic loads (free vibration, stationary random excitation as well as nonstationary random excitation, with single component or multi-component), and the optimum operating regions are all determined. The amount of dissipated energy due to impact and friction, and the concept of “Effective Momentum Exchange” are shown to be suitable “global” measures to interpret the physics involved in the behavior of particle dampers. Using the well-established discrete element method, the motion of vertical particle dampers can be analyzed and classified into three different regions, and the associated damping characteristics can be interpreted. The first mode of a MDOF primary system can be effectively controlled by a properly designed particle damper; however, the higher modes are more affected by other parameters. Consequently, extensive parametric studies are presented to evaluate the effects of various system parameters, such as: mass ratio, primary system damping, coefficient of restitution, container dimensions, excitation amplitude and components, input locations and damper locations.     

The transmission of vertical vibration through seats: Influence of the characteristics of the human body

The transmission of vibration through a seat depends on the impedance of the seat and the apparent mass of the seat occupant. This study was designed to determine how factors affecting the apparent mass of the body (age, gender, physical characteristics, backrest contact, and magnitude of vibration) affect seat transmissibility. The transmission of vertical vibration through a car seat was measured with 80 adults (41 males and 39 females aged 18-65) at frequencies between 0.6 and 20 Hz with two backrest conditions (no backrest and backrest), and with three magnitudes of random vibration (0.5, 1.0, and 1.5 m s^-2 rms). Linear regression models were used to study the effects of subject physical characteristics (age, gender, and anthropometry) and features of their apparent mass (resonance frequency, apparent mass at resonance and at 12 Hz) on the measured seat transmissibility. The strongest predictor of both the frequency of the principal resonance in seat transmissibility and the seat transmissibility at resonance was subject age, with other factors having only marginal effects. The transmissibility of the seat at 12 Hz depended on subject age, body mass index, and gender. Although subject weight was strongly associated with apparent mass, weight was not strongly associated with seat transmissibility. The resonance frequency of the seat decreased with increases in the magnitude of the vibration excitation and increased when subjects made contact with the backrest. Inter-subject variability in the resonance frequency and transmissibility at resonance was less with greater vibration excitation, but was largely unaffected by backrest contact. A lumped parameter seat-person model showed that changes in seat transmissibility with age can be predicted from changes in apparent mass with age, and that the dynamic stiffness of the seat appeared to increase with increased loading so as to compensate for increases in subject apparent mass associated with increased sitting weight.     

Semi-active on–off damping control of a dynamic vibration absorber using Coriolis force

A passive dynamic vibration absorber (DVA) moving along a pendulum can cause the nonlinear Coriolis damping to reduce the pendulum swing. This paper proposes a simple semi-active on–off damping controller to improve the passive Coriolis DVA. The aim of the on–off damping control is to amplify the DVA resonance motion to increase the energy dissipated. Moreover, the paper finds the analytical solution of the harmonic vibration of semi-active controlled system. The accuracy of the analytical formulas and the superior performance of the semi-active DVA are verified by numerical simulations.     

Analytical and experimental validation of a nondimensional Bingham model for mixed-mode magnetorheological dampers

In this paper an experimental validation of a nondimensional analysis for a mixed-mode magnetorheological (MR) damper is described. Based on the Bingham constitutive equation of an MR fluid, a nondimensional model describing damping capacity of the MR damper is formulated using nondimensional parameters including the Bingham number, nondimensional plug thickness, hydraulic amplification ratio, and equivalent viscous damping coefficient. The effects of the Bingham number and the hydraulic amplification ratio on the nondimensional plug thickness and equivalent viscous damping coefficient are analyzed. A mixed-mode MR damper is designed and fabricated to validate the relationships between nondimensional parameters. The damper is tested under various loading conditions and current (applied magnetic field intensity) levels. The nondimensional parameters and variables are measured experimentally, and the effectiveness of the nondimensional analysis model for mixed-mode MR dampers is demonstrated. In addition, comparisons between mixed and flow mode dampers are undertaken using this nondimensional analysis.     

EFFECTS RELATED TO RANDOM WHOLE-BODY VIBRATION AND POSTURE ON A SUSPENDED SEATWITH AND WITHOUT BACKREST

WBV-exposures are often linked with forced postures as prolonged sitting, bent forward sitting, or sitting without a backrest. No quantitative data are available to describe the exposure-effect relationships for different conditions of seating, posture, and the biological variability of workers. Experiments and subsequent predictions of forces acting within the spine during WBV can help to improve the assessment of the health risk. An experimental study was performed with 39 male subjects sitting on a suspension seat with or with no backrest contact. They were exposed to random whole-body vibration with a weighted r.m.s. value of 0·6 m/s² at a relaxed or a forward bending posture. A two-dimensional finite element model was used for the calculation of the internal spinal load. The model simulates the human response on a suspension driver seat. Individual exposure conditions were considered by including the transfer functions between the seat cushion and the seat base as well as between the backrest and the seat base for the calculation of the vibration input to the buttocks and to the back respectively. The average peak seat transmissibility was higher for the seat with the backrest, but the peak seat-to-head transmissibility was higher for the seat without the backrest for both postures. The peak transmissibilities between the accelerations at the seat base and the compressive forces at L5/S1 were highest for the seat without the backrest during the bending posture. Various biological effects can result from identical exposures combined with different backrest contact and postures. The backrest contact and posture conditions should not be neglected in the assessment of health risk caused by whole-body vibration.     

EVALUATING THE VIBRATION ISOLATION OF SOFT SEAT CUSHIONS USING AN ACTIVE ANTHROPODYNAMIC DUMMY

Seat test standards require human subjects to be used for measuring the vibration isolation of vehicle seats. Anthropodynamic dummies, based on passive mass-spring- damper systems, have been developed for testing seats but their performance has been limited at low excitation magnitudes by non-linear phenomena, such as friction in the mechanical components that provide damping. The use of an electrodynamic actuator to generate damping forces, controlled by feedback from acceleration and force transducers, may help to overcome these limitations and provide additional benefits. The transmissibilities of five foam cushions have been measured using an actively controlled anthropodynamic dummy, in which damping and spring forces were supplied by an electrodynamic actuator. The dummy could be set up to approximate alternative single-degree-of-freedom and two-degree-of-freedom apparent mass models of the seated human body by varying motion feedback parameters. Cushion transmissibilities were also measured with nine human subjects, having an average seated weight similar to the dummy. At frequencies greater than 4 Hz, mean cushion transmissibilities measured with subjects were in closer agreement with the transmissibilities obtained with a two degree-of-freedom dummy than with a single degree-of-freedom dummy. However, at frequencies between 2 and 4 Hz, cushion transmissibilities obtained with the two-degree-of-freedom dummy showed consistently larger differences from mean transmissibilities with subjects than single-degree-of-freedom dummies, indicating a need for further development of human apparent mass models to account for the effects of magnitude and spectral content of the input motion. Vertical vibration isolation efficiencies (SEAT values) of the five foams were measured with four input motions, including three motions measured in a car. The SEAT values obtained using the active dummy were highly correlated with the median SEAT values obtained with the nine human subjects, with the two-degree-of-freedom apparent mass dummy giving the highest agreement.     

Extending the dynamic range of an energy harvester using nonlinear damping

This paper introduces the use of nonlinear damping for extending the dynamic range of vibration energy harvesters. A cubic nonlinear damper is initially considered and the average harvested power and the throw are obtained for different sinusoidal base excitation amplitudes and frequencies, both numerically and analytically. It is demonstrated that when excited at resonance, at an amplitude below its maximum operational limit, the harvested power using a nonlinear damper can be significantly larger than that of a linear energy harvester, therefore expanding its dynamic range. A potential approach to implementing cubic nonlinearity using a shunted electromagnetic device is also presented.