Prediction of Damping Capacity Demand in Seismic Base Isolators via Machine Learning

Base isolators used in buildings provide both a good acceleration reduction and structural vibration control structures.The base isolators may lose their damping capacity over time due to environmental or dynamic effects.This deterioration of them requires the determination of the maintenance and repair needs and is important for the long-termisolator life.In this study,an artificial intelligence prediction model has been developed to determine the damage and maintenance-repair requirements of isolators as a result of environmental effects and dynamic factors over time.With the developed model,the required damping capacity of the isolator structure was estimated and compared with the previously placed isolator capacity,and the decrease in the damping property was tried to be determined.For this purpose,a data set was created by collecting the behavior of structures with single degrees of freedom(SDOF),different stiffness,damping ratio and natural period isolated from the foundation under far fault earthquakes.The data is divided into 5 different damping classes varying between 10%and 50%.Machine learning model was trained in damping classes with the data on the structure’s response to random seismic vibrations.As a result of the isolator behavior under randomly selected earthquakes,the recorded motion and structural acceleration of the structure against any seismic vibration were examined,and the decrease in the damping capacity was estimated on a class basis.The performance loss of the isolators,which are separated according to their damping properties,has been tried to be determined,and the reductions in the amounts to be taken into account have been determined by class.In the developed prediction model,using various supervised machine learning classification algorithms,the classification algorithm providing the highest precision for the model has been decided.When the results are examined,it has been determined that the damping of the isolator structure with the machine learning method is predicted successfully at a level exceeding 96%,and it is an effective method in deciding whether there is a decrease in the damping capacity.

Effects of Fatigue Characteristics on Static and Dynamic Performance of Eucommia Rubber Isolators

This study aimed to investigate the effect of fatigue characteristics on the static and dynamic performance of Eucommia ulmoides gum isolators, and to explore the performance changes of Eucommia ulmoides gum isolators with different formulations. For this purpose, we used five formulations of Eucommia ulmoides gum isolators and set different fatigue test methods to study the static and dynamic performance changes of Eucommia ulmoides gum isolators with different formulations by changing the amplitude. The experimental results showed that the addition of Eucommia ulmoides gum had an impact on the performance of the isolator, and the number of fatigue cycles would lead to the hardening of the Eucommia ulmoides gum isolator and changes in its static and dynamic performance. In the range of two million vibrations, the performance change of the isolator was significant in the early stage and then tended to be flat, indicating that the impact of fatigue on the performance of the isolator would not continue to persist. It is worth noting that the study found that the addition of 30% Eucommia ulmoides gum had the least impact on the performance of the isolator under fatigue. Therefore, for long-term use of Eucommia ulmoides gum isolators, attention should be paid to their fatigue characteristics to ensure their stability and reliability. Additionally, this study provides a reference for the design and application of Eucommia ulmoides gum isolators. In summary, this study provides important reference value for a deeper understanding of the fatigue characteristics of Eucommia ulmoides gum isolators and for ensuring their stable and reliable performance. .

Frequency domain analysis of pre-stressed elastomeric vibration isolators

Two types of elastomeric vibration isolators used for equipment vibration isolation in aerospace vehicles are considered for the present study. These isolators are constructed using elastomers mounted in steel encasings. These isolators are initially deformed statically and dynamic loads are applied on the deformed configuration. To capture the static deformation, equivalent static load corresponding to its load rating and specified displacements are created. Static deformation is computed using Finite Element methods with four node axi-symmetric element which include the geometric non-linear effect for steel and with standard Yeoh hyper-elastic material model for elastomers(Muhammed and Zu, 2012) [1]. Yeoh material constants are derived from uni-axial tension test data of the elastomer specimen. These isolators are subjected to harmonic and random excitations in the pre-deformed state. For numerical analysis, elastomeric constants at dynamic conditions are obtained as complex function of frequency using Dynamic Mechanical Analyzer(DMA) for a range of frequencies. The standard material model of Yeoh is modified incorporating frequency dependant material characteristics and damping in the range of frequencies of interest. A multiplicative non-separable variables law is derived for Yeoh material model to include the effect of static pre-stress, based on the methodology given in literature(Nashif et al.,1985;Beda et al., 2014) [2,3]. The modifications of Yeoh model suitable for frequency domain analysis is the novelty in the present study. In the analysis, while dynamic loads are applied, the configuration is updated considering initial static loading. The frequency response of the isolators is computed using material properties evaluated at progressive dynamic strains until a match in natural frequency is observed. Appropriate damping corrections are then incorporated to match the test observed transmissibility. Then updated material properties are used to compute the random response which showed good agreement with results of experiments, validating the approach taken for the development of this model.

EFFECTS OF INCOMING FLOW ASYMMETRY ON SHOCK TRAIN STRUCTURES IN CONSTANT-AREA ISOLATORS

To simulate the actual flowfield at the exit of the supersonic/hypersonic inlet, a wind tunnel is designed to study the flow in the scramjet isolator under the asymmetric incoming flow. And compression fields in the isolator are investigated using wall static and pitot pressure measurements. Three incoming Mach numbers are considered as 1.5, 1.8 and 2. Results show that the increase of the asymmetry of the flow at the isolator entrance leads to the increase of the shock train length in the isolator for a given pressure ratio. Based on the analysis of the flow asymmetry effect at the isolator entrance on the shock train length, a modified correlation is proposed to calculate the length of the shock train. Predicted results of the proposed correlation are in good agreement with the experimental data.

Mechanical properties of disc-spring vibration isolators based on boundary friction

To ascertain the influence of the boundary friction on mechanical properties of disc-spring vibration isolators a load-displacement hysteresis curve formula of disc-spring vibration isolators is derived on the basis of the energy conservation law as well as considering the effect of the boundary friction.The formula is validated through the finite element analysis and static load tests.On this basis the effect of the boundary friction on the bearing capacity is researched. Then the dynamic performance of disc-spring vibration isolators is studied by dynamic tests.The experimental results indicate that the boundary friction can promise a larger damping with a ratio of 0.23 for disc-spring vibration isolators.Compared with the loading frequency the loading amplitude has a greater impact on the energy consumption dynamic stiffness and damping of vibration isolators.This research can provide valuable information for the design of disc-spring vibration isolators.

Modeling,analysis,and simulation of X-shape quasi-zero-stiffness-roller vibration isolators

Existing quasi-zero stiffness(QZS)isolators are reviewed.In terms of their advantages,a novel X-shape QZS isolator combined with the cam-roller-spring mechanism(CRSM)is proposed.Different from the existing X-shape isolators,oblique springs are used to enhance the negative stiffness of the system.Meanwhile,the CRSM is used to eliminate the gravity of the loading mass,while the X-shape structure leaves its static position.The existing QZS isolators are demonstrated and classified according to their nonlinearity mechanisms and classical shapes.It is shown that the oblique spring can realize negative stiffness based on the simplest mechanism.The X-shape has a strong capacity of loading mass,while the CRSM can achieve a designed restoring force at any position.The proposed isolator combines all these advantages together.Based on the harmonic balance method(HBM)and the simulation,the displacement transmissibilities of the proposed isolator,the X-shape isolators just with oblique springs,and the X-shape isolators in the traditional form are studied.The results show that the proposed isolator has the lowest beginning isolation frequency and the smallest maximum displacement transmissibility.However,it still has some disadvantages similar to the existing QZS isolators.This means that its parameters should be designed carefully so as to avoid becoming a bistable system,in which there are two potential wells in the potential energy curve and thus the isolation performance will be worsened.

Numerical investigation of the seismic response of a UHV composite bypass switch retrofitted with wire rope isolators

An ultra-high voltage(UHV)composite bypass switch(BPS)faces increasing seismic challenges when UHV projects extend to high seismic intensity areas.The UHV composite BPS still generates excessive stress at the bottom section although hollow composite insulators with high flexural strength are adopted.Since the standard retrofitting strategy by using stiffer supports cannot reduce stress responses,wire rope isolation is introduced.The optimal design of isolation considers both stress and displacement responses since the slenderness and composite material of insulators contribute to significant displacement.The results show that properly designed isolation can significantly reduce stress without excessive displacement responses.A larger radius configuration helps to improve the applicability of small stiffness isolators under high winds.When the isolation still cannot satisfy the requirement,smaller stiffness isolators with a larger radius,or isolators with increased loops and smaller radius,can be introduced to gain better energy dissipation capacity and effectiveness in response mitigation.Accordingly,a three-step design procedure is proposed to increase the damping force but fix the rotational stiffness of isolation.Hence,the application of wire rope isolation can be extended to UHV composite BPS with a low natural frequency,but conductors with enough redundancy should be used.

Polynomial friction pendulum isolators(PFPIs)for seismic performance control of benchmark highway bridge

The seismic response of a benchmark highway bridge isolated with passive polynomial friction pendulum isolators （PFPIs） is investigated and subjected to six bidirectional ground motion records. The benchmark study is based on a lumped mass finite-element model of the 91/5 highway overcrossing located in Southern California. The PFPI system possesses two important parameters; one is horizontal flexibility and the other is energy absorbing capacity through friction. The evaluation criteria of the benchmark bridge arc analyzed considering two parameters, time period of the isolator and coefficient of friction of the isolation surface. The results of the numerical study are compared with those obtained from the traditional friction pendulum system （FPS）. Dual design performance of the PFPI system suppressed the displacement and acceleration response of the benchmark highway bridge. The dual design hysteresis loop of the PFPI system is the main advantage over the linear hysteresis loop of the FPS. The numerical result indicates that the seismic performance of the PFPI system is better than that of the traditional FPS isolated system. Further, it is observed that variations of the isolation time period and coefficient of friction of the FPS and PFPI systems have a significant effect on the peak responses of the benchmark highway bridge.

Pseudo-Dynamic Testing for Seismic Performance Assessment of Buildings with Seismic Isolation System Using Scrap Tire Rubber Pad Isolators

Investigation of seismic performance of buildings with STRP （scrap tire rubber pad） seismic isolators by means of pseudo-dynamic tests and numerical simulation is presented. The isolated building is numerically modeled, while the base isolation layer is considered as the experimental substructure in the pseudo-dynamic tests. The test result verifies that the STRP isolator shows acceptable shear deformation performance predicted by the design methods, and demonstrated that seismic isolation using STRP works as a protective measure to provide enhanced seismic performance of the building indicated by the reduction of top floor absolute acceleration, drift and base shear as designated.

CALCULATION OF ELASTIC-DAMPING CHARACTERISTICS OF MULTI-LAYER STEEL STRIPE VIBRATION ISOLATORS

Theoretical and experimental research on multi-layer steel plates isolatorare exploited. The relationship between the thickness, width, number of layers, radius, numbers ofthe rings, stiffness, inner friction force, energy dissipation coefficient of isolator are derived,and a mathematie model of hysteresis loop of isolator is obtained. Experimental results show thatthe calculation equation and mathematie model of hysteresis loop can satisfy with experimentalresults very well.

Lateral load performance and seismic demand of unbonded scrap tire rubber pad base isolators

The scrap tire rubber pad(STRP)made by natural or synthetic rubber and high strength reinforcing cords exhibits substantial vertical stiffness and horizontal flexibility,and these properties can be regarded as suitable for seismic isolators for structures.The use of environmentally burdensome scrap tires as STRP isolators might be convenient as an efficient and low-cost solution for the implementation of aseismic design philosophy for low-to-medium rise buildings,especially in developing countries.Finite element analyses of unbonded square and strip-shaped STRP isolators subjected to a combination of axial and lateral loads are conducted to investigate its lateral deformation performance under seismic loading.The rubber of the isolator is modelled with Mooney-Rivlin hyperelastic and Prony viscoelastic materials,including the Mullins material damage effect.The influence of the length-to-width ratio and bearing height on the isolator performance is assessed in terms of the force-displacement relationship,horizontal stiffness,damping,and isolation periods.It is shown that the dependence of stiffness on the length-to-width ratio is significant in the longitudinal direction and minor in the transverse direction.The STRP isolators following the proposed design criteria are shown to satisfy the performance requirement at different levels of seismic demand specified by the ASCE/SEI 7-2010 seismic provisions.

Using a SVM to evaluate damage to vibration isolators in an elastic raft system

Predicting damage to vibration isolators in a raft experiencing heavy shock loadings from explosions is an important task when designing a raft system. It is also vital to be able to research the vulnerability of heavily shocked floating rafts unreliable, especially when the allowable values The conventional approach to prediction has been or ultimate values of vibration isolators of supposedly uniform standard in a raft actually have differing and uncertain values due to defective workmanship. A new model for predicting damage to vibration isolators in a shocked floating raft system is presented in this paper. It is based on a support vector machine（SVM）, which uses Artificial Intelligence to characterize complicated nonlinear mapping between the impacting environment and damage to the vibration isolators. The effectiveness of the new method for predicting damage was illustrated by numerical simulations, and shown to be effective when relevant parameters of the model were chosen reasonably. The effect determining parameters, including kernel function and penalty factors, has on prediction results is also discussed. It can be concluded that the SVM will probably become a valid tool to study damage or vulnerability in a shocked raft system.

Synchrophasing Vibration Control of Machines Supported by Discrete Isolators

This paper describes an analytical investigation into synchrophasing,a vibration control strategy on a machinery installation in which two rotational machines are attached to a beam-like raft by discrete resilient isolators.Forces and moments introduced by sources are considered,which effectively represent a practical engineering system.Adjusting the relative phase angle between the machines has been theoretically demonstrated to greatly reduce the cost function,which is defined as the sum of velocity squares of attaching points on the raft at each frequency of interest.The effect of the position of the machine is also investigated.Results show that altering the position of the secondary source may cause a slight change to the mode shape of the composite system and therefore change the optimum phase between the two machines.Although the analysis is based on a one-dimensional Euler– Bernoulli beam and each machine is considered as a rigid-body,a key principle can be derived from the results.However,the factors that can influence the synchrophasing control performance would become coupled and highly complicated.This condition has to be considered in practice.

A Damping Characteristics Calculation Method of Metal Dry Friction Isolators

The dry friction ring-type vibration isolator is considered as an isotropic continuous medium. A method of dry friction hysteresis loop calculation is proposed based on friction force analysis of contact beam. The friction force is modeled as an equivalent distributed moment to use the finite element method （FEM） to calculate the dry friction vibration isolator hysteresis loop, so the damping characteristics can be obtained. A comparison of the hysteresis loop calculation results and the experimental results shows the average relative error is 2.7 %, it proves the calculation method is feasible.

Research on low-frequency mechanical characteristics of the MR dampers in ship isolators

A new isolator composed of a steel rope spring and a magneto-rheological(MR) damper was designed and a study on low-frequency mechanical characteristics of MR dampers in isolators was carried out.It used the characteristics of the MR damper,such as fast response,controllable damping,small energy consumption,wide dynamic scope,and great adaptation.The relationships between MR damping forces and influencing factors were analyzed based on experimental data.The results show that damping force is not only related to structural dimensions,but also closely related to controllable current and vibration frequency.Finally,the empirical formula for damping forces was corrected,and the relationship between correction coefficients and factors analyzed.

Parameter Identification of Rubber Isolators Using Frequency-Dependent Spring and Damper Coefficients

A model to describe the hysteresis damper character of rubber material is presented in this paper. It consists of a parallel spring and damper, whose coefficients change with vibration frequencies. In order to acquire these relations, the force decomposition is carried out according to some sine vibration measurement data about nonlinear forces changing with deformations of the rubber material. The nonlinear force is decomposed into a spring force and a damper force, which are represented by a frcquency-dependent spring and damper coefficient, respectively. Repeating this step for different measurements will give different coefficients corresponding to different frequencies. Then, application of a parameter identification method will provide the requested functions over frequency. Using those formulae, as an example, the dynamic character of a hollow shaft system supported by rubber rings is analyzed and the acceleration response curve in the centroid position is calculated. Comparisons with sine vibration experiments of the real system show a maximal inaccuracy of 8. 8 %. Application of this model and procedure can simplify the modeling and analysis of mechanical systems including rubber materials.

Material Model Research on Rubber Vibration Isolators

A viscohyperelastic constitutive model is proposed to describe the mechanical behaviour of vibration isolation rubber under broad-band vibration. This constitutive model comprises two parts： a component with three parameters to characterize the hyperelastic static properties of rubber materials, and the other component incorporating two relaxation time parameters, corresponding to high and low strain rates, respectively, to describe the dynamic response under vibration and impact loadings. Based on this proposed constitutive model, a series of experiments were performed on two types of rubber materials over a wide strain rate range. The results predicted from this model are in good agreement with the experimental data.

Design of low-frequency circular metastructure isolators with high-load-bearing capacity

Traditional vibration isolation structures cannot work effectively for low-frequency vibration under heavy loads,due to the inherent contradiction between the high-static and lowdynamic stiffness of these structures.Although the challenge can be effectively addressed by introducing a negative stiffness mechanism,the existing structures inevitably have complex configurations.Metastructures,a class of man-made structures with both extraordinary mechanical properties and simple configurations,provide a new insight for low-frequency vibration isolation technology.In this paper,circular metastructure isolators consisting of some simple beams are designed for low-frequency vibration,including a single-layer isolator and a double-layer isolator,and their static and dynamic characteristics are studied,respectively.For the static characteristic,the force–displacement and stiffness–displacement curves are obtained by finite element simulation;for the dynamic characteristic,the vibration transmissibility curves are obtained analytically and numerically.The result shows that the circular nonlinear single-layer isolator has excellent lowfrequency isolation performance,and the isolation frequency band will decrease about 20 Hz when the isolated mass is fixed at 1.535 kg,compared with a similar circular linear isolator.These static and dynamic properties are well verified through experiments.Our work provides an innovative approach for the low-frequency vibration isolation and has wide potential applications in aeronautics.

Isolation performances and optimization of triple quasi-zero stiffness isolators

In this paper,triple quasi-zero stiffness(QZS)passive vibration isolators whose restoring force curve has a three-stage softening effect are proposed.Multi-coupled SD oscillators with three independent geometrical parameters are used as negative stiffness mechanisms to achieve QZS characteristics at the origin and symmetrical positions on both sides of the origin.Isolation performances of different triple QZS isolators are analyzed to show influences of the selection of QZS regions away from the origin on the range of isolation regions.Pareto optimizations of system parameters are carried out to get a larger range of small restoring force regions and small stiffness regions.Isolation performances of two triple QZS isolators are discussed to show the influence of different Pareto optimization solutions through the comparisons with single and double QZS isolators.Results showed that triple QZS isolators have both the advantages of single and double QZS isolators which results in better isolation performances under both small and large excitation amplitudes.An improvement in isolation performances for triple QZS isolators is found with the decrease in average stiffness due to the appearance of two symmetrical QZS regions away from the origin.Larger displacements of QZS regions away from the origin result in better isolation performances when excitation amplitude is large,and triple QZS characteristics are similar to double QZS isolators at this time.Smaller restoring forces of QZS regions away from the origin lead to better isolation performances when excitation amplitude is small,and triple QZS characteristics are similar to single QZS isolators at this moment.Compared with the decrease in average stiffness,the improvement of isolation performances shows a hysteresis phenomenon due to the difference between static and dynamic characteristics.

A review on magneto-optical ceramics for Faraday isolators

As a promising magneto-optical(MO)material applied in Faraday isolators,magneto-optical ceramics possess excellent comprehensive properties and have attracted much attention these years.Herein,we review the fabrication and properties of magneto-optical ceramics including garnet,sesquioxide,and A_(2)B_(2)O_(7) ceramics.Some of the ceramics have been proved to possess applicable performance,while further studies are still needed for most of the magneto-optical ceramics.Aiming at the application for isolators,the research status,existing problems,and development trends of magneto-optical ceramics are shown and discussed in this review.