Experiment and analysis of a fuzzy-controlled piezoelectric seismic isolation system

Because a conventional seismic isolation system is usually a long-period dynamic system, it may easily incur an excessive seismic response when subjected to near-fault earthquakes, which usually contain strong long-period wave components. In order to alleviate this near-fault isolation problem, this paper investigates the possible use of a fuzzy-controlled semi-active isolation system, called a piezoelectric seismic isolation system (PSIS), whose seismic response is attenuated by a variable friction damper driven by an embedded piezoelectric actuator. The studied PSIS adopts a fuzzy controller whose control logic is similar to that of the anti-lock braking systems (ABS) widely used in the automobile industry. This ABS-type fuzzy controller has the advantages of being simple and easily implemented, because it only requires the measurement of the PSIS sliding velocity. In order to investigate its feasibility and isolation effectiveness, in this work both theoretical and experimental studies were carried out on a prototype PSIS. It is observed that the experimental responses of the PSIS can be well predicted by the theoretical responses simulated by the mathematical model and numerical procedure. Furthermore, both theoretical and experimental results have demonstrated that in either a near-fault or a far-field earthquake, the PSIS with the ABS-type fuzzy controller is very effective in suppressing simultaneously the isolator displacement and the acceleration response of the isolated object.     

Research on performance indices of vibration isolation system

Power flow transmissibility is proposed as a performance index to evaluate the performance of isolation system. It is defined as the ratio of the power flow input into the equipment and the power flow transmitted into the receiver. Based on a simple vibration isolation system, its relationship with other performance indices is given by theoretical and numerical analysis. The results show that power flow transmissibility can reflect the response characteristics of the whole isolation system effectively. In addition, power flow transmissibility can be estimated easily according to vibration acceleration level difference and does not involve the measurement of power flow. Furthermore, the influences of several parameters such as the damping, loss factor and stiffness of isolator on power flow transmissibility are analyzed.     

Vibration isolation via a scissor-like structured platform

More and more attentions are attracted to the analysis and design of nonlinear vibration control/isolation systems for better isolation performance. In this study, an isolation platform with n-layer scissor-like truss structure is investigated to explore novel design of passive/semi-active/active vibration control/isolation systems and to exploit potential nonlinear benefits in vibration suppression. Due to the special scissor-like structure, the dynamic response of the platform has inherent nonlinearities both in equivalent damping and stiffness characteristics (although only linear components are applied), and demonstrates good loading capacity and excellent equilibrium stability. With the mathematical modeling and analysis of the equivalent stiffness and damping of the system, it is shown that: (a) the structural nonlinearity in the system is very helpful in vibration isolation, (b) both equivalent stiffness and damping characteristics are nonlinear and could be designed/adjusted to a desired nonlinearity by tuning structural parameters, and (c) superior vibration isolation performances (e.g., quasi-zero stiffness characteristics etc.) can be achieved with different structural parameters. This scissor-like truss structure can potentially be employed in different engineering practices for much better vibration isolation or control.     

Active pneumatic vibration isolation system using negative stiffness structures for a vehicle seat

In this paper, an active pneumatic vibration isolation system using negative stiffness structures (NSS) for a vehicle seat in low excitation frequencies is proposed, which is named as an active system with NSS. Here, the negative stiffness structures (NSS) are used to minimize the vibratory attraction of a vehicle seat. Owing to the time-varying and nonlinear behavior of the proposed system, it is not easy to build an accurate dynamic for model-based controller design. Thus, an adaptive intelligent backstepping controller (AIBC) is designed to manage the system operation for high-isolation effectiveness. In addition, an auxiliary control effort is also introduced to eliminate the effect of the unpredictable perturbations. Moreover, a radial basis function neural network (RBFNN) model is utilized to estimate the optimal gain of the auxiliary control effort. Final control input and the adaptive law for updating coefficients of the approximate series can be obtained step by step using a suitable Lyapunov function. Afterward, the isolation performance of the proposed system is assessed experimentally. In addition, the effectiveness of the designed controller for the proposed system is also compared with that of the traditional backstepping controller (BC). The experimental results show that the isolation effectiveness of the proposed system is better than that of the active system without NSS. Furthermore, the undesirable chattering phenomenon in control effort is quite reduced by the estimation mechanism. Finally, some concluding remarks are given at the end of the paper.     

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.     

Equivalent linear stochastic seismic response of isolated bridges

Stochastic response of bridges seismically isolated by lead-rubber bearings (LRB) is investigated. The earthquake excitation is modeled as a non-stationary random process (i.e. uniformly modulated broad-band excitation). The stochastic response of isolated bridge is obtained using the time-dependent equivalent linearization technique as the force-deformation behavior of the LRB is highly nonlinear. The non-stationary response of isolated bridge is compared with the corresponding stationary response in order to study the effects of non-stationary characteristics of the earthquake input motion. For a given isolated bridge system and excitation, it was observed that there exists an optimum value of the yield strength of LRB for which the root mean square (rms) absolute acceleration of bridge deck attains the minimum value. The optimum yield strength of LRB is investigated under important parametric variations such as isolation period and damping ratio of the LRB and the frequency content and intensity of earthquake excitation. It is shown that the above parameters have significant effects on the optimum yield strength of LRB. Finally, closed-form expressions for the optimum yield strength of LRB and corresponding response of the isolated bridge system are proposed. These expressions were derived based on the model of bridge with rigid deck and pier condition subjected to stationary white-noise excitation. It was observed that there is a very good comparison between the proposed closed-form expressions and actual optimum parameters and response of the isolated bridge system. These expressions can be used for initial optimal design of seismic isolation system for the bridges.     

Application of broadband nonlinear targeted energy transfers for seismic mitigation of a shear frame: Computational results

In this work we show that it is possible to successfully apply the concept of nonlinear targeted energy transfer (TET) to seismic protection of structures; moreover, this passive strategy of seismic vibration control is found to be feasible and robust. We consider a three-story shear-frame structure, modeled as a three-degree-of-freedom system, subjected to four historic earthquakes as seismic excitation. Seismic mitigation is achieved by applying single or multiple nonlinear energy sinks (NESs) to the test structure. We study the performance and efficiency of the NESs through a set of evaluation criteria. First we consider a single vibro-impact NES (VI NES) applied to the top floor of the structure. In order to assess the robustness of the VI NES, the NES parameters are optimized for a specific seismic excitation (Kobe), and then tested against the three other earthquake records to demonstrate effectiveness of the NES for these cases as well. To further improve the effectiveness of the seismic mitigation, we then consider a system of two NESs—an NES with smooth nonlinearity at the top floor of the test structure and a VI NES at the bottom floor. We show that it is indeed possible to drastically reduce the structural seismic response (e.g., displacements, drifts, and accelerations) using this configuration.     

Transverse hysteretic damping characteristics of a serpentine belt: Modeling and experimental investigation

In this paper, the transverse dynamic hysteretic damping characteristics (HDC) of a serpentine belt are investigated. The variable stiffness and variable damping model (VSDM) constituted of a variable-stiffness spring and a variable-damping damper is developed to estimate the HDC of the belt. A test rig is designed to test the force–displacement hysteresis damping curve and resonance frequencies of serpentine belts with different lengths under diverse loading conditions. The force–displacement hysteresis damping curve getting from the experiment is then used to determine the transverse stiffness and damping coefficients needed for the VSDM. The experiment particularly shows that the orientation of the hysteresis curve swings left and right around each natural frequency as it is a symmetrical point. This interesting phenomenon is explicated in detail with the loss angle which is calculated by two methods. Moreover, two sub-analytical models included in the VSDM are proposed to model the dependence of transverse dynamic stiffness and damping coefficient of a belt on belt length, pretension and excitation frequency. A comparison of the hysteresis curves obtained from the VSDM and experiment indicates that they are in good agreement.     

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.     

Dynamic isolation systems using tunable nonlinear stiffness beams

Vibration isolation devices are required to reduce the forcing into the supporting structure or to protect sensitive equipment from base excitation. A suspension system with a low natural frequency is required to improve isolation, but with linear supports the minimum stiffness is bounded by the static stiffness required to support the equipment. However, nonlinear high-static-low-dynamic-stiffness (HSLDS) mounts may be designed, for example by combining elastic springs in particular geometries, to give the required nonlinear force-displacement characteristics. Current approaches to realise the required nonlinear characteristics are often inconvenient. Furthermore, the weight of the supported equipment, the environment, or the structural stiffness may change. This paper investigates the design of HSLDS isolation mounts using beams of tunable geometric nonlinear stiffness. In order to obtain the nonlinear response required, we first study the case of generic beams subject to static loads that are able to tune their nonlinear force-displacement characteristics to ensure that the isolators have very low dynamic stiffness. Tuning is achieved by actuators at the ends of the beams that prescribe the axial displacement and rotation. Secondly, we study a composite beam with an initial thermal pre-stress, resulting in internal stresses that give the required nonlinear response.     

Shock isolation using an isolator with switchable stiffness

A semi-active control strategy is presented for the shock isolation of resiliently mounted equipment where the isolator has light damping. This is achieved by switching the stiffness of the isolator between a high-state and a low-state. The control strategy involves two stages: the first stage involves the displacement control of the equipment during the shock, and the second stage involves suppression of the subsequent residual vibrations. The performance of the switchable isolation system is illustrated using a base-excited single degree-of-freedom system. It is characterized in terms of the maximum absolute acceleration and displacement of the isolated mass, the relative displacement between the base and the mass, and the effective damping ratio of the system. Provided that the damping in the isolator is light, it is found that the semi-active system can outperform a linear passive system during both stages of control.     

An experimental switchable stiffness device for shock isolation

The development of an experimental switching stiffness device for shock isolation is presented. The system uses magnetic forces to exert a restoring force, which results in an effective stiffness that is used to isolate a payload. When the magnetic force is turned on and off, a switchable stiffness is obtained. Characterization of the physical properties of the device is presented. They are estimated in terms of the percentage stiffness change and effective damping ratio when switched between two constant stiffness states. Additionally, the setup is used to implement a control strategy to reduce the shock response and minimize residual vibration. The system was found to be very effective for shock isolation. The response is reduced by around 50 percent compared with passive isolation showing good correlation with theoretical predictions, and the effective damping ratio in the system following the shock was increased from about 4.5 percent to 13 percent.     

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.     

Modelling and dynamic properties of a novel solid and liquid mixture vibration isolator

Solid and Liquid Mixture (SALiM) vibration isolator is a new isolator which is designed for vibration isolation of heavy equipment with low frequency. The isolator contains liquid and elastic solid elements as working media. To get the stiffness property of the isolator, this paper establishes the mechanics model of elastic solid elements by introducing plate-shell model. Considering geometry nonlinearity, the stiffness of the element under outer liquid pressure and inner air pressure was obtained by perturbation method. Then the stiffness of isolator is derived. As a result, the stiffness is piecewise linear-nonlinear and determined by parameters of the elastic elements and elastic container. In addition, the equation of motion (EOM) of a single degree of freedom system supported by a SALiM isolator is given. The properties of the frequency response function (FRF) of the system are analysed using averaging method which is a classical approximation approach for estimating nonlinear system FRF. And it is found that the system with SALiM isolator shows softening stiffness behaviour. The jumping phenomenon clearly occurs under certain condition. Finally, the vibration isolation property is predicted based on energy transmissibility (ET) in different cases.     

Joining of components of complex structures for improved dynamic response

The goal of this work is to provide a method for choosing joining (e.g., bolt) locations for attaching structural reinforcements onto complex structures. The joining locations affect structural performance criteria such as the frequency response and the static compliance of the modified structure. One approach to finding improved/optimal joining locations is to place the joints such that the total amount of energy input into the structure (from external forces) is lowered/minimized, thus ensuring that the performance of the structure is least affected by the structural modifications. However, such an approach does not account for the stresses in the joints. Therefore, in this work, the amount of strain energy concentrated in the joints is also considered. The cost function for this optimization problem is then composed of two energies. These energies are different for the undamped and damped cases. Herein, the focus is on the (more realistic) damped case. The cost function is minimized by a modified optimality criteria method. This process is time consuming because it requires the calculation of sensitivities of the joint strain energy, which in turn requires the calculation of the displacements of all candidate joint locations by using the system-level mass and stiffness matrices and force vector (at each frequency in the range of interest). To address this issue, a series of complex algebraic manipulations and approximations are used to significantly reduce the computational cost. In addition, for the case where structural and geometrical variations are necessary, parametric reduced-order models are used to compute the cost function with further significant gains in computational speed. Numerical results for improved/optimal joining are presented for representative complex structures with structural variabilities.     

A vibration isolation system in low frequency excitation region using negative stiffness structure for vehicle seat

This paper designs and fabricates a vibration isolation model for improving vibration isolation effectiveness of the vehicle seat under low excitation frequencies. The feature of the proposed system is to use two symmetric negative stiffness structures (NSS) in parallel to a positive stiffness structure. Here, theoretical analysis of the proposed system is clearly presented. Then, the design procedure is derived so that the resonance peak of frequency-response curve drifts to the left, the load support capacity of the system is maintained, the total size of the system is reduced for easy practical application and especially, the bending of the frequency-response curve is minimized. Next the dynamic equation of the proposed system is set up. Then, the harmonic balance (HB) method is employed to seek the characteristic of the motion transmissibility of the proposed system at the steady state for each of the excitation frequency. From this characteristic, the curves of the motion transmission are predicted according to the various values of the configurative parameters of the system. Then, the time responses to the sinusoidal, multi frequency and random excitations are also investigated by simulation and experiment. In addition, the isolation performance comparison between the system with NSS and system without NSS is realized. The simulation results reveal that the proposed system has larger frequency region of isolation than that of the system without NSS. The experimental results confirm also that with a random excitation mainly spreading from 0.1 to 10 Hz, the isolation performance of the system with NSS is greatly improved, where the RMS values of the mass displacement may be reduced to 67.2%, whereas the isolation performance of the system without NSS is bad. Besides, the stability of the steady-state response is also studied. Finally, some conclusions are given.     

一种光电载荷非线性隔振装置的研究

针对光电载荷对隔振性能的需求,提出一种采用菱形连杆机构作为负刚度组件,具有高静、低动刚度特点的非线性隔振器（简称菱形HSLDS隔振器）。采用静力学分析方法,建立了隔振器数学模型,研究了刚度参数设定以及非线性调节方法;利用谐波平衡法（HBM）求解动力学方程,分析了各参数对隔振性能的影响关系;采用动力学仿真软件ADAMS及实物样机对理论模型与结论进行了验证。测试结果表明:菱形HSLDS隔振器具有较方便的参数调整能力,零位刚度及刚度非线性可通过拉簧参数与连杆参数进行设定、优化,隔振的刚度非线性优化程度受主隔振器阻尼以及零位刚度参数影响。相比于传统线性隔振器,菱形HSLDS具有显著的非线性隔振优势,可较好地满足光电载荷隔振需求。     

Vibration isolation characteristics of a nonlinear isolator using Euler buckled beam as negative stiffness corrector: A theoretical and experimental study

This paper concerns the vibration isolation characteristics of a nonlinear isolator using Euler buckled beams as negative stiffness corrector. Both analytical and experimental studies are carried out. The Harmonic Balance Method (HBM) is used to determine the primary resonance response for the single degree of freedom (SDOF) nonlinear system composed by a loaded mass and the nonlinear isolator. The distuning of the loaded mass is taken into consideration, resulting in a Helmoholtz–Duffing equation. The performance of the nonlinear isolator is evaluated by the defined two kinds of transmissibility and compared with that of the linear isolator without the stiffness corrector. The study shows that the asymmetric SDOF nonlinear system can behave like a purely softening, a softening–hardening or a purely hardening system, depending on the magnitude of the excitation level. An experimental apparatus is set up to validate the analytical results. The transmissibility results of the SDOF nonlinear system under base excitation with both discrete sinusoidal frequencies and slowly forward and backward sweeps are given and discussed. The complex jump phenomena under different excitation levels are identified. By introducing the stiffness corrector, the starting frequency of isolation of the nonlinear isolator is found to be lower than that of the linear one with the same support capacity. The proposed nonlinear isolator performs well in applications where the excitation amplitude is not too large.     

Nonlinear analysis,design and vibration isolation for a bilinear system with time-delayed cubic velocity feedback

This paper combines cubic nonlinearity and time delay to improve the performance of vibration isolation. Nonlinear dynamics properties, design methodology and isolation performance are studied for a piecewise bilinear vibration isolation system with the time-delayed cubic velocity feedback control. By the multi-scale perturbation method, the equivalent stiffness and damping are first defined to interpret the effect of feedback control loop on dynamics behaviours, such as frequency island phenomenon. Then, a design criterion is proposed to suppress the jump phenomenon induced by the saddle-node bifurcation. With the purpose of obtaining the desirable vibration isolation performance, stability conditions are obtained to find appropriate feedback parameters including gain and time delay. Last, the influence of the feedback parameters on vibration transmissibility is assessed. Results show that the strategy developed in this paper is practicable and feedback parameters are significant factors to alter dynamics behaviours, and more importantly, to improve the isolation effectiveness for the bilinear isolation system.     

Stability and performance limits for active vibration isolation using blended velocity feedback

This paper presents a theoretical study of active vibration isolation on a two degree of freedom system. The system consists of two lumped masses connected by a coupling spring. Both masses are also attached to a firm reference base by a mounting spring. The lower mass is excited by a point force. A reactive control force actuator is used between the two masses in parallel with the coupling spring. Both masses are equipped with an absolute velocity sensor. The two sensors and the actuator are used to implement velocity feedback control loops to actively isolate the upper mass from the vibrations of the lower mass over a broad range of frequencies. The primary concern of the study is to determine what type of velocity feedback configuration is suitable with respect to the five parameters that characterise the system (the three spring stiffnesses and the two masses). It is shown analytically that if the ratio of the lower mounting spring stiffness to the lower mass is larger than the ratio of the upper mounting spring stiffness to the upper mass (supercritical system), feeding back the absolute upper mass velocity to the reactive force actuator results in an unconditionally stable feedback loop and the vibration isolation objective can be fully achieved without an overshot at higher frequencies. In contrast, if the ratio of the lower mounting spring stiffness to the lower mass is smaller than the ratio of the upper mounting spring stiffness to the upper mass (subcritical system), the upper mass velocity feedback is conditionally stable and the vibration isolation objective cannot be accomplished in a broad frequency band. For subcritical systems a blended velocity feedback is proposed to stabilise the loop and to improve the broad-band vibration isolation effect. A simple inequality is introduced to derive the combinations between the two error velocities that guarantee unconditionally stable feedback loops.