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.     

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.     

Damping performance of two simple oscillators coupled by a visco-elastic connection

A simple dynamic system composed of two linear oscillators is employed to analyze the passive control performance that can be achieved through a visco-elastic damper connecting two adjacent free-standing structures. By extension, the model may also describe the energy dissipation which can be obtained by an internal coupling between two quasi-independent sub-systems composing a single complex structure. Two alternatives are evaluated for the linear coupling by considering either the serial or the parallel spring–dashpot arrangement known as the Kelvin–Voigt and the Maxwell damper model, which may synthetically reproduce the constitutive behavior of different industrial devices. The complex eigenvalues of the coupled system are parametrically analyzed to determine the potential benefits realized by different combinations of the coupling stiffness and damping coefficient. A design strategy to assess these parameters is outlined, driven by the relevant observation that a perfect tuning of the natural frequencies always corresponds, in the parameter space, to the maximum modal damping for one of the resonant modes, independent of the damper model. The effectiveness of the proposed strategy is discussed for different classes of the controlled system, depending on the mass and stiffness ratio of the component oscillators. As a major result, different design parameter charts for the two damper models are carried out and compared to each other. Performance indexes are introduced to quantitatively evaluate the passive control performance with respect to the mitigation of the system forced response under harmonic and seismic ground excitation. The analyses confirm the validity of the design strategy for a well-balanced mitigation of the displacement and acceleration response in both the oscillators.     

EVALUATION OF VIBRATION AND SHOCK ATTENUATION PERFORMANCE OF A SUSPENSION SEAT WITH A SEMI-ACTIVE MAGNETORHEOLOGICAL FLUID DAMPER

The potential benefits of a semi-active magnetorheological (MR) damper in reducing the incidence and severity of end-stop impacts of a low natural frequency suspension seat are investigated. The MR damper considered is a commercially developed product, referred to as “Motion Master semi-active damping system” and manufactured by Lord Corporation. The end-stop impact and vibration attenuation performance of a seat equipped with such a damper are evaluated and compared with those of the same seat incorporating a conventional damper. The evaluation is performed on a servo-hydraulic vibration exciter by subjecting the seat-damper combinations to a transient excitation with dominant frequency close to that of the seat and continuous random excitation class EM1 applicable to earth-moving machinery, and a more severe excitation realized by amplifying the EM1 excitation by 150%. Tests are performed for medium and firm settings of the MR damper and for seat height positions corresponding to mid-ride and ±2·54 and ±5·08 cm relative to mid-ride. The results indicate that significantly higher levels of transient excitation are necessary to induce end-stop impacts for the seat equipped with the MR damper, particularly when set for firm damping, the difference with the conventional damper being more pronounced for seat positions closer to the end-stops. Under the EM1 excitation, the results indicate that under conditions which would otherwise favour the occurrence of end-stop impacts for a seat equipped with a conventional damper, the use of the MR damper can result in considerably less severe impacts and correspondingly lower vibration exposure levels, particularly when positioned closer to its compression or rebound limit stop.     

Optimum connecting dampers to reduce the seismic responses of parallel structures

Parameters of connecting dampers between two adjacent structures and twin-tower structure with large podium are optimized through theoretical analysis. The connecting visco-elastic damper (VED) is represented by the Kelvin model and the connecting viscous fluid damper (VFD) is represented by the Maxwell model. Two optimization criteria are selected to minimize the vibration energy of the primary structure and to minimize the vibration energy of both structures. Two representative numerical examples of adjacent structures and one three-dimensional finite element model of a twin-tower with podium structure are used to verify the correctness of the theoretical approach. On the one hand, by means of theoretical analysis, the first natural circular frequencies and total mass of the two structures can be taken as parameters in the general formula to get the optimal parameters of the coupling dampers. On the other hand, using the Kanai-Tajimi filtered white-noise ground motion model and several actual earthquake records, the appropriate parameters of two types of linking dampers are obtained through extensive parametric studies. By comparison, it can be found that the results of parametric studies are consistent with the results of theoretical studies for the two types of dampers under the two optimization criteria. The effectiveness of VED and VFD is investigated in terms of the seismic response reduction of the neighboring structures. The numerical results demonstrate that the seismic response and vibration energy of parallel structures are mitigated significantly. The performances of VED and VFD are comparable to one another. The explicit formula of VED and VFD can help engineers in application of coupled structure control strategies.     

Extended Kalman filter for modal identification of structures equipped with a pendulum tuned mass damper

Pendulum tuned mass dampers (PTMDs) have been employed in several full-scale applications to attenuate excessive structural motions, which are mostly due to wind. Conducting periodic condition assessments of the devices to ascertain their health is necessary to ensure their continued optimal performance, which involves identifying the modal parameters of the underlying (bare) structure to which they are tuned to. Such an identification is also necessary for the design of control systems such as adaptive tuned mass dampers. Existing methods of arresting the motion of the damper to estimate the modal properties are expensive, time-consuming, and not suitable for online tuning. Instead, in this paper, parameter estimation using the Extended Kalman Filter (EKF) is proposed to undertake this task. The central task accomplished here is to estimate the dynamic characteristics of the bare structure (structure without the PTMD) from response measurements of the coupled main structure and PTMD system. The proposed methodology relies on ambient acceleration measurements of TMD-attenuated responses to estimate the bare structural modal frequencies, damping, and mode shapes, which can then be used either for condition assessment or for control. The application of EKF to modal parameter estimation is not new. However, a methodology to address the problem in wind engineering arising from stochastic disturbances present in both the measurement and state equations, and unknown process and noise covariances arising due to ambient excitations, is presented for the first time. Extensively studied for synthetic data, these two challenges have limited thus far the application of Kalman filtering to practical wind engineering parameter estimation problems using experimentally obtained measurements. In this paper, a detailed methodology is presented to address these challenges by using a modified form of the standard EKF equations, together with an algorithm to estimate the unknown disturbance and measurement noise covariances. Numerical simulations and an experimental study are both presented. Results demonstrate that the method proposed provides reliable estimates for the modal parameters required to perform condition assessment and control tasks for pendulum tuned mass dampers.     

Performance analysis of nonlinear vibration isolator with magneto-rheological damper

A nonlinear vibration isolator is considered to study effectiveness of isolation against harmonic force and displacement excitations. Nonlinearity in the magneto-rheological (MR) fluid based damper as well as in the elastic member is taken into account. The MR-damper has been modeled including Bouc–Wen hysteretic element and the spring is taken to have cubic nonlinearity. Analytical expression for the energy dissipation characteristics of the damper has been derived. Near resonant response of the isolated mass is obtained by a modified averaging technique suitable for hysteretic type nonlinearity present in the system. The performance of the isolators is estimated for various nonlinear stiffness values, both hardening and softening types. Different performance measures are also proposed to judge the performance of the nonlinear isolator.     

Combined primary–secondary system approach to the design of an equipment isolation system with High-Damping Rubber Bearings

Isolating acceleration-sensitive equipment from the motion of the supporting structure represents an effective protection from earthquake damage. In this paper, a passive equipment isolation system composed of High-Damping Rubber Bearings (HDRB) is designed by adopting a coupled approach in which the supporting structure and the isolated equipment are considered as parts of a combined primary–secondary system and analyzed together. This allows for taking into account their dynamic interaction when significant and non-negligible according to the mass ratio and to the frequency ratio. The design methodology is developed by resorting to a reduced-order 2-DOF model of the combined system, a linear visco-elastic constitutive model of the isolation system and to a modal damping constraint depending upon the damping properties of the HDRB and their rubber compound. A 1:5 scale experimental model, consisting of a two-storey steel frame and a heavy block-type mass isolated from the second floor, is subsequently used to exemplify the design methodology and to perform shaking table tests. The dynamic properties of the experimental model are identified and the seismic performance of the equipment isolation system is discussed under a wide selection of seismic inputs, both artificial and natural.     

Proportional-plus-integral semiactive control using magnetorheological dampers

Magnetorheological (MR) dampers are a promising alternative to structural active actuators as they provide adjustable damping over a wide range of frequencies without large power requirements. However, the complex dynamics that characterizes these devices makes it difficult to formulate control laws based on the MR damper model. Instead, many semiactive control strategies proposed in the literature have been based on the idea of “clipping” the voltage signal so that the MR damper force “tracks” a desired active control force which is computed on-line. With this idea many algorithms have been proposed using, among others, techniques such as optimal control, H_∞ control, sliding mode control, backstepping and QFT.This work presents a semiactive control strategy based on the same idea of “clipping” the voltage signal but using a simpler PI design. The proportional and integral gains of the controller are calculated so that the controller guarantees stability, minimization of the closed loop response and robustness against modeling errors. Effectiveness of the control strategy is compared to some others techniques and passive cases as well. Simulation results shows that this simple strategy can effectively improve the structural responses and achieve performance index comparable to that of more complex algorithms.     

液幕式吸收塔中传质模型研究

对液幕式吸收塔脱硫性能进行了实验研究,研究了烟气流量、循环浆液量、浆液浓度,喷嘴阵列形式等参数对脱硫性能的影响,合理选择装置结构和运行参数时,脱硫效率可达90%以上;提出了液幕式吸收塔中当量传质面积的计算方法,建立了液幕式吸收塔的传质模型,得到了液幕式吸收塔的传质系数关于气相和液相雷诺数及喷嘴阵列的经验关系式。     

Vibration suppression of a cantilever beam using magnetically tuned-mass-damper

Eddy currents are induced by the movement of a conductor through a stationary magnetic field or a time varying magnetic field through a stationary conductor. These currents circulate in the conductive material and are dissipated, causing a repulsive force between the magnet and the conductor. These electromagnetic forces can be used to suppress the vibrations of a flexible structure. A tuned mass damper is a device mounted in structures to reduce the amplitude of mechanical vibrations and is one of the effective vibration suppression methods. In the present study, an improved concept of this tuned mass damper for the vibration suppression of structures is introduced. This concept consists of the classical tuned mass damper and an eddy current damping. The important advantages of this magnetically tuned mass damper are that it is relatively simple to apply, it does not require any electronic devices and external power, and it is effective on the vibration suppression. The proposed concept is designed for a cantilever beam and the analytical studies on the eddy current damping and its effects on the vibration suppression. To show the effectiveness of the proposed concept and verify the eddy current damping model, experiments on a cantilever beam are performed. It is found that the proposed concept could significantly increase the damping effect of the tuned mass damper even if not adequately tuned.     

Multifunctional design of inertially-actuated velocity feedback controllers

The vibration of a structure can be controlled using either a passive tuned mass damper or using an active vibration control system. In this paper, the design of a multifunctional system is discussed, which uses an inertial actuator as both a tuned mass damper and as an element in a velocity feedback control loop. The natural frequency of the actuator would normally need to be well below that of the structure under control to give a stable velocity feedback controller, whereas it needs to be close to the natural frequency of a dominant structural resonance to act as an effective tuned mass damper. A compensator is used in the feedback controller here to allow stable feedback operation even when the actuator natural frequency is close to that of a structural mode. A practical example of such a compensator is described for a small inertial actuator, which is then used to actively control the vibrations both on a panel and on a beam. The influence of the actuator as a passive tuned mass damper can be clearly seen before the feedback loop is closed, and broadband damping is then additionally achieved by closing the velocity feedback loop.     

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。     

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利用有限元仿真软件ANSYS Workbench,结合反应谱法对ITER极向场变流器外旁通设备进行了地震分析。具体分析了在ITER提供的设计地震频谱下,外旁通结构所受的最大等效应力、方向位移以及固定支撑位置的反作用力。分析结果表明,外旁通最大等效应力不超过8.3MPa,最大方向位移不超过2.6mm。以上数据表明,外旁通结构能够满足抗震要求。     

ITER极向场变流器外旁通设备地震分析

利用有限元仿真软件ANSYS Workbench,结合反应谱法对ITER极向场变流器外旁通设备进行了地震分析。具体分析了在ITER提供的设计地震频谱下,外旁通结构所受的最大等效应力、方向位移以及固定支撑位置的反作用力。分析结果表明,外旁通最大等效应力不超过8.3MPa,最大方向位移不超过2.6mm。以上数据表明,外旁通结构能够满足抗震要求。     

A STOCHASTIC OPTIMAL SEMI-ACTIVE CONTROL STRATEGY FOR ER/MR DAMPERS

A stochastic optimal semi-active control strategy for randomly excited systems using electrorheological/magnetorheological (ER/MR) dampers is proposed. A system excited by random loading and controlled by using ER/MR dampers is modelled as a controlled, stochastically excited and dissipated Hamiltonian system with n degrees of freedom. The control forces produced by ER/MR dampers are split into a passive part and an active part. The passive control force is further split into a conservative part and a dissipative part, which are combined with the conservative force and dissipative force of the uncontrolled system, respectively, to form a new Hamiltonian and an overall passive dissipative force. The stochastic averaging method for quasi-Hamiltonian systems is applied to the modified system to obtain partially completed averaged Itô stochastic differential equations. Then, the stochastic dynamical programming principle is applied to the partially averaged Itô equations to establish a dynamical programming equation. The optimal control law is obtained from minimizing the dynamical programming equation subject to the constraints of ER/MR damping forces, and the fully completed averaged Itô equations are obtained from the partially completed averaged Itô equations by replacing the control forces with the optimal control forces and by averaging the terms involving the control forces. Finally, the response of semi-actively controlled system is obtained from solving the final dynamical programming equation and the Fokker-Planck-Kolmogorov equation associated with the fully completed averaged Itô equations of the system. Two examples are given to illustrate the application and effectiveness of the proposed stochastic optimal semi-active control strategy.     

Hysteretic tuned mass dampers for structural vibration mitigation

The hysteresis exhibited by short steel wire ropes is shown to lend itself as an effective restoring force for nonlinear monodirectional tuned mass dampers. Experiment-driven modeling based on the identified hysteretic restoring forces together with continuation tools enables an optimal design of these dampers through construction of families of frequency–response curves over a wide range of excitation amplitudes. Semi-analytical/numerical and experimental studies are carried out considering a base-excited test structure represented by a simply supported beam together with a prototype of the hysteretic damper subject to either harmonic or filtered Gaussian white noise excitations.     

The optimization of mechanical dampers to control self-excited galloping oscillations

The use of mechanical dampers for the control of the self-excited galloping of transmission lines is considered. Two particular dampers, an in-span damper and a resilient mounting, are studied, two mass representations being used. For both dampers it is possible to produce an optimum damper either by maximizing the negative damping excitation that the damped system can withstand, or by choosing the smaller logarithmic decrement of oscillation of the system to be as large as possible in the absence of excitation. These two procedures do not produce the same damper parameters. Simple analytical expressions are produced for the optimum parameters, and these are shown to agree well with numerically optimized parameters. For the in-span damper, either method of optimization gives a damper for a much wider range of ratios of the damper to conductor masses than is predicted by earlier work. For the resilient mounting the optimization based on damping gives very similar behaviour to that of the in-span damper. When aerodynamic excitation is considered for the resilient mounting, a clear optimum exists only for a small range of mass ratios. Results from a representation of the conductor by a stretched string are used to define the range of mass ratios over which the two-mass damper idealizations may be used to define damper properties.     

Novel schemes for inserting seismic dampers in shear-type systems based upon the mass proportional component of the Rayleigh damping matrix

This paper presents the results of an extensive study carried out to investigate the applicability of a novel scheme for inserting added viscous dampers in shear-type systems. The findings, even though developed with specific reference to civil building structures, provide useful insight also for the effective addition of viscous dampers in mechanical dynamic systems (of similar characteristics) when excited at the base.The novel scheme proposed (referred to as the MPD system) is based upon the mass proportional component of the Rayleigh damping matrix (MPD matrix) and is characterised by a peculiar damper placement which sees the dampers placed so that they connect each mass to a fixed point.Firstly, the paper briefly recalls (a) the physical principles and (b) selected results of numerical investigations which show that the MPD system is characterised by superior dissipative properties.Secondly, the paper investigates the implementation of the MPD system in civil building structures. Two solutions are envisaged herein: direct implementation (through the use of long buckling-resistant dampers which connect each storey to the ground) and indirect implementation (by placing common dampers between the structure and a very stiff lateral-resisting element adjacent or internal to the structure). The first solution leads to the implementation in the structure of an exact MPD matrix, if damper sizing is chosen appropriately. The second solution (simpler than the first one to implement in building structures) leads to an exact MPD matrix, if, in addition to appropriate damper sizing, the lateral-resisting element is infinitely stiff. As far as the direct implementation is concerned, this paper shows how long buckling-resistant braces are available for structural systems up to three storey high. As far as the indirect implementation is concerned, this paper shows (through extensive numerical parametric investigations) how this solution is capable of providing damping effects which are similar to those offered by the direct implementation, even for lateral-resisting elements characterised by finite lateral stiffness. The results obtained also provide insight for the optimal insertion of viscous dampers in coupled mechanical dynamic systems.     

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。