Variable Frequency Pendulum Isolator Research Articles

Seismic Performance of Irregular Building with different Variable sliding isolators and Semi active Dampers

The comparative performances of semiactive friction and stiffness dampers with different control laws in the base-isolated Irregular building subjected to bi-directionally acting strong earthquakes have been studied. The Irregular building is hybridly isolated with rubber bearings and friction pendulum system (FPS) or variable frequency pendulum isolator (VFPI) or variable curvature friction pendulum system (VCFPS). The shear type base-isolated Irregular building is modeled as three-dimensional linear elastic structure having three degrees-of-freedom at each floor level. Time domain dynamic analysis of the building has been carried out with the help of constant average acceleration Newmark-Beta method and non-linear isolation forces has been taken care by fourth-order Runge-Kutta method. The effects of variation of characteristic properties of semiactive dampers on their hysteresis loops and on the structural response of Irregular building is studied through parametric study. Comparative performances of different semiactive dampers with sliding isolation systems for seismic control of Irregular building have been observed through time history plots and peak response performance indices. It has been found that semiactive electromagnetic friction damper work efficiently with VFPI and VCFPS in comparison FPS for the Irregular building for near field earthquakes as it not only reduces base displacement at lower control force but also give lower base shear and story drift in base-isolated Irregular building. The control laws based on modulated homogeneous friction control semiactive friction dampers better than the predictive control law.

Application of MR damper in Base-isolated Irregular Building with different variable sliding Isolators

Application of Electromagnetic induction (EMI) based passively controlled and some local response governed MR dampers in controlling the isolator displacement in base-isolated Irregular building have been studied and compared with the Lyapunov controller. The Irregular building is hybrid isolated with elastomeric rubber bearings and a variety of sliding isolators subjected to strong near field earthquakes acting bi-directionally in horizontal plane. The shear type base-isolated Irregular building is modelled as three-dimensional linear elastic structure having three degrees-of-freedom at each floor level. Time domain dynamic analysis of the building has been carried out using constant-average acceleration Newmark-Beta method and non-linear isolation forces has been taken care by fourth-order Runge-Kutta method. It is observed that the EMI based passive controller performs better than the Lyapunov controller though it reduces less base displacement but gives lower structural response among all the controllers. Local response governed Hyperbolic and Aly’s controller require only velocity and displacement at controller locations sound simpler in application as compared to Lyapunov controller especially to civil engineering structures like Irregular building. The Hyperbolic controller restrains base displacement comparable to the Lyapunov controller but gives less base shear and story drifts to Irregular building. Variable frequency pendulum isolator (VFPI) and variable curvature friction pendulum system (VCFPS) sliding isolators perform better with MR damper control in comparison to conventional friction pendulum system (FPS) in base–isolated Irregular building.

Response Prediction of VFPI Through Equivalent Long Period Wavelet of Near-Fault Ground Motion

Past research has revealed that a Variable Frequency Pendulum Isolator (VFPI) effectively controls the structural responses such as base shear and structural acceleration under far and near fault earthquakes and the VFPI may show excessive sliding displacement under some earthquakes having 4-6 s time-period long waves. But, the impact of the amplitude of the long period wave on the sliding displacement of VFPI is missing in past research due to difficulty in finding out the amplitude of long period wave of an earthquake. Therefore, the present study considered the amplitude of the long period wave of an earthquake to analyse the behaviour of the structure isolated by VFPI. For this, the most dangerous long period wave of earthquakes has been extracted in the form of noise free wavelets by using Mavroeidis and Papageorgiou proposed numerical approach. The results indicate that the noise free long period wavelet effectively represent the low frequency earthquake for the structure isolated by VFPI. It is also found out that, the VFPI shows the excessive sliding displacement for only those earthquakes which contains peak ground displacement of long period wave more than 0.40 m. The variation in the base shear and structural acceleration of structure isolated by VFPI under various value of Frequency Variation Factor (FVF) obey the exponential and cubic form respectively. According to this, the present research provides empirical formulas, chart, and tables to predict the structural and isolator responses by using the peak ground velocity (PGV) and dominating low frequency (fd) of a near fault earthquake.

Seismic resistant design of highway bridge with multiple-variable frequency pendulum isolator

Multiple variable frequency pendulum isolator (MVFPI) has been recently developed as a superior alternative to the traditional friction pendulum bearing (FPB) especially for the seismic isolation in near-fault regions. The MVFPI is characterized by its variable frequency and self-adaptability, which are achieved by piecewise function of sliding surface and shape memory alloy (SMA). The objective of this study is to propose the design algorithm of the MVFPIs in highway bridge as an extension of the direct displacement-based design (DDBD) framework. The nonlinearities of the structural components are taken into account in the design procedure, and the corresponding damage states satisfy the two-stage design philosophy. The accuracy and robustness of the design procedure are verified by an isolated four-span highway bridge through nonlinear time history (NLTH) analyses. The analytical results indicate that the proposed design procedure can predict the profile of deck displacement and amplitude, as well as the damage states of the piers. From statistic aspect, the fragility analyses illustrate that the bridge isolated by MVFPIs exhibits better seismic performance than that of the bridge isolated by FPBs.

Effectiveness of sliding isolators with variable curvature in near‐fault ground motions

SummaryRecent studies have revealed that a sliding isolator with variable curvature (SIVC) can mitigate the resonance phenomenon likely to occur in seismic response of a conventional friction pendulum system (FPS) isolator due to its constant isolation frequency. The present study simulates four SIVC isolators and an FPS to find the optimum range of initial isolation period and coefficient of friction and employ them in comparing the effectiveness of SIVC in different peak ground acceleration (PGA) scales of near‐fault earthquakes. Velocity‐dependent coefficient of friction and modified viscoplasticity model have been used to simulate nonlinear friction force of the isolators. Results indicate identical performance of all SIVC isolators in PGA scales up to 0.4 g. When subjected to PGA scales from 0.4 g to 1.0 g, polynomial friction pendulum isolator (PFPI) and variable curvature friction pendulum system (VCFPS) reduce base displacement greatly, while conical friction pendulum isolator (CFPI) and variable frequency pendulum isolator (VFPI) show amplified responses. However, in mitigating structural acceleration, performance of CFPI and VFPI, unlike PFPI and VCFPS, which perform poorly, is excellent. Thus, in a strong near‐fault earthquake, PFPI and VCFPS or CFPI and VFPI can be chosen based on whether reduction of base displacement or super‐structural acceleration is the main concern of designer, respectively. Copyright © 2015 John Wiley & Sons, Ltd.

Performance of variable curvature sliding isolators in base‐isolated benchmark building

AbstractThe performances of variable curvature sliding isolators like variable frequency pendulum isolator (VFPI) and variable curvature friction pendulum system (VCFPS) installed in the base‐isolated benchmark building subjected to bi‐directionally acting seven strong earthquakes have been studied. The shear type base‐isolated benchmark building is modelled as three‐dimensional linear elastic structure having three degrees‐of‐freedom at each floor level. Time domain dynamic analysis of the building has been carried out with the help of constant average acceleration Newmark‐Beta method and non‐linear isolation forces has been taken care by fourth‐order Runge‐Kutta method. The force‐displacement responses of the VFPI and VCFPS are studied under parametric variations of their key characteristics for the comparative performance evaluation. The time history variations of response characteristics and peak response evaluation criteria are also investigated for overall comparison of their performances. The performance of VFPI and VCFPS are observed both in uniform and hybrid isolation systems. The force‐displacement responses of both VFPI and VCFPS subjected to strong near‐field earthquakes show excessively large isolator displacements at higher initial radii of curvature of sliding surface. The large isolator displacements of VFPI and VCFPS can be restrained efficiently by addition of viscous fluid dampers in comparison to the increase in coefficient of friction of isolators. Copyright © 2010 John Wiley & Sons, Ltd.

Seismic Isolation of Bridges with Double Variable Frequency Pendulum Isolator

The paper describes behaviour of multi-span continuous deck bridge isolated by the double variable frequency pendulum isolator (DVFPI). The governing equations of motion of the bridge-isolation system subjected to bilateral ground excitation are derived and solved in the incremental form. In order to investigate the behaviour of the DVFPI, the response is obtained under different parametric variations for a set of nine far-fault earthquake ground motions with low, medium and high intensities. Four different combinations of the DVFPI design cases having different isolator geometry and coefficient friction at top and bottom sliding surfaces are studied and the criterion to optimize its performance is proposed based on minimum responses and energy quantities. It is found that the performance of the DVFPI can be optimized by designing the top sliding surface with high initial stiffness relative to the bottom one and the coefficient of friction of both sliding surfaces to be equal.

Control of seismically excited benchmark highway bridge with variable frequency pendulum isolator

Earthquake response of benchmark highway bridge, isolated with variable frequency pendulum isolator (VFPI) is investigated under six earthquakes, using a simplified lumped mass finite element model. The isolators are installed between deck-ends and abutments. Seismic response of the bridge with VFPI is compared with that of the bridge with the friction pendulum system (FPS). Parametric studies are carried to find the optimum values of coefficient of friction and isolation period of the FPS; and frequency variation factor, initial time period and coefficient of friction of VFPI. The response of the bridge with VFPI is compared with the uncontrolled case, with FPS, and that controlled by alternate sample control strategies. Significant reductions in base shear, base moment, deck displacements and bearing displacements are observed using FPS and VFPI. It is concluded that these isolators are quite effective in substantially reducing peak response quantities of the bridge, comparable to that of the sample controllers.

Seismic response of liquid storage steel tanks with variable frequency pendulum isolator

The seismic response of liquid storage steel tanks (slender and broad) isolated with Variable Frequency Pendulum Isolators (VFPIs) is investigated under normal component of six near-fault ground motions. The continuous liquid mass is lumped as convective mass, impulsive mass and rigid mass. The corresponding stiffness associated with these lumped masses is worked out depending upon the properties of the tank wall and liquid mass. The frictional forces mobilized at the interface of the VFPI are assumed to be velocity independent. The governing equations of motion of liquid storage steel tanks isolated with the VFPIs are derived and solved in the incremental form using Newmark’s step-by-step method assuming linear variation of acceleration over small time interval. For comparative study, the seismic response of liquid storage steel tanks with the VFPIs is compared with that of the same liquid storage steel tanks isolated using the Friction Pendulum Systems (FPSs). In order to measure the effectiveness of isolation system, the seismic response of isolated steel tanks is compared with that of the non-isolated steel tanks. Further, a parametric study has been carried out to critically examine the behaviour of liquid storage steel tanks isolated with VFPIs. The important parameters considered are the friction coefficient of the VFPI, the Frequency Variation Factor (FVF) of the VFPI and the tank aspect ratio. The difference between the liquid storage tanks isolated with the VFPI and the FPS isolators subjected to the harmonic and far-field ground motions was also investigated in this study. Effect of vertical component of ground motions on the behaviour of the VFPI-isolated liquid storage tanks is investigated under triaxial ground excitations by considering the interaction of forces in two orthogonal directions. From these investigations, it is concluded that seismic response, viz. the base shear, the sloshing displacement and the impulsive displacement, of liquid storage steel tanks during near-fault ground motions can be controlled within a desirable range with the installation of the VFPI. Under strong harmonic excitations, the base shear of the VFPI reduces than that of the FPS whereas the sloshing displacement, the impulsive displacement and the isolator displacement of the VFPI exceeds than that of the FPS. It is also found that the isolation by the FPS and VFPI isolators has almost the same effect in the tank to the far-field ground motions. The triaxial ground motions have noticeable effect on the response of the VFPI-isolated liquid storage tanks relative to unilateral ground motion and if ignored, the sliding displacement and base shear will be underestimated.

Double variable frequency pendulum isolator for seismic isolation of liquid storage tanks

The paper describes the behaviour of liquid storage slender and broad tanks isolated by the double variable frequency pendulum isolator (DVFPI). The DVFPI is a double sliding isolation system having elliptical sliding surfaces. The geometry and coefficient of friction of top and bottom sliding surfaces can be unequal. The governing equations of motion and energy balance equation of the tank-isolation system subjected to bilateral ground excitation are derived and solved in the incremental form. In order to investigate the behaviour of the DVFPI, the response is obtained under different parametric variations for a set of 20 far-field earthquake ground motions. Four different combinations of the DVFPI design cases having different isolator geometry and coefficient friction at top and bottom sliding surfaces are studied and the criterion to optimize its performance is proposed based on minimum responses and energy quantities. Further, influences of the initial time period, coefficient of friction and frequency variation factors at the two sliding surfaces and the tank aspect ratio are investigated. It is found that the performance of the DVFPI can be optimized by designing the top sliding surface with high initial stiffness relative to the bottom one and the coefficient of friction of both sliding surfaces to be equal for a slender tank whereas both surfaces should be designed with equal initial stiffness and coefficient of friction for a broad tank.

Seismic Response of Base-Isolated Benchmark Building with Variable Sliding Isolators

The seismic response of base-isolated benchmark building with variable sliding isolators like variable friction pendulum system (VFPS), variable frequency pendulum isolator (VFPI), and variable curvature friction pendulum system (VCFPS), along with conventional friction pendulum system (FPS), was studied under the seven earthquakes. The earthquakes are applied bi-directionally in the horizontal plane ignoring vertical ground motion component. The shear type base-isolated benchmark building is modeled as three-dimensional linear elastic structure having three degrees of freedom at each floor level. Time domain dynamic analysis of the benchmark building was carried out with the help of constant average acceleration Newmark-Beta method and nonlinear isolation forces was taken care by fourth-order Runge-Kutta method. The base-isolated benchmark building is investigated for uniform isolation and hybrid isolation in combination with laminated rubber bearings through the performance criteria and time history response of important structural response parameters like floor accelerations, base displacement, etc. It is observed that variable sliding isolators performed better than conventional FPS due to their varying characteristic properties which enable them to alter the isolator forces depending upon their isolator displacements thus improves the performance of the structure. The VFPS efficiently controls large isolator displacements and VFPI and VCFPS improve super structural response on the cost of isolator displacement. It is also observed that the hybrid isolation is relatively better in comparison to the uniform isolation for the benchmark building.

Response of the Double Variable Frequency Pendulum Isolator under Triaxial Ground Excitations

Modeling techniques of double variable frequency pendulum isolator (DVFPI) are presented. Seismic responses of the three-dimensional single-story building isolated by DVFPI with different coefficient of friction and initial time period of top and bottom sliding surfaces are investigated under triaxial ground motions and compared with unilateral and bilateral ground excitations. Furthermore, the influence of vertical flexibility on horizontal response is also investigated. It is observed that the triaxial ground motion has noticeable effect on response of the building relative to unilateral ground motion. The error in peak resultant base shear, occurring by neglecting vertical ground motion component, could be significant.

Seismic response of the double variable frequency pendulum isolator

The double variable frequency pendulum isolator (DVFPI) is an adaptation of single variable frequency pendulum isolator (VFPI). The principle benefit of the DVFPI is its capacity to accommodate larger displacements compared to the VFPI of identical plan dimensions. Moreover, there is the capability to use sliding surfaces with varying isolator geometry and coefficients of friction of top and bottom sliding surfaces, giving the designer greater flexibility to optimize performance. This paper describes the mathematical modeling and force–displacement relationships of the DVFPI. Behavior of the DVFPI is studied by varying isolator geometry and coefficient of friction of the two sliding surfaces and criteria to optimize the performance of the DVFPI are proposed. Further, influences of the initial time period, the coefficient of friction and the frequency variation factors at the two sliding surfaces are investigated. The combined effect of change in the initial time period and the coefficient of friction on the seismic response of the DVFPI is also studied. It is observed that the best performance of the DVFPI can be achieved by designing it with different friction coefficient and different initial time period of the two sliding surfaces. Copyright © 2010 John Wiley & Sons, Ltd.

Behaviour of asymmetric building with double variable frequency pendulum isolator

Presented in this paper is the behaviour of asymmetric building isolated by the double variable frequency pendulum isolator (DVFPI). The DVFPI is an adoption of single variable frequency pendulum isolator (VFPI). The geometry and coefficient of friction of top and bottom sliding surfaces can be unequal. The governing equations of motion of the building-isolation system are derived and solved in incremental form. The analysis duly considers the interaction of frictional forces in the two principal directions developed at each sliding surface of the DVFPI. In order to investigate the behaviour of the base isolation using the DVFPI, the coupled lateral-torsional response is obtained under different parametric variations for a set of six far-fault earthquake ground motions and criterion to optimize its performance is proposed. Further, influences of the initial time period, coefficient of friction and frequency variation factors at the two sliding surfaces are investigated. The numerical results of the extensive parametric study help in understanding the torsional behaviour of the structure isolated with the double sliding surfaces as in the DVFPI. It is found that the performance of the DVFPI can be optimized by designing the top sliding surface initially softer and smoother relative to the bottom one.

Seismic behavior of variable frequency pendulum isolator

Earthquake performance of a flexible one-story building isolated with a variable frequency pendulum isolator (VFPI) under near-fault and far-field ground motions is investigated. The frictional forces mobilized at the interface of the VFPI are assumed to be velocity dependent. The interaction between frictional forces of the VFPI in two horizontal directions is duly considered and coupled differential equations of motion of the isolated system in the incremental form are solved iteratively. The response of the system with bi-directional interaction is compared with those without interaction. In addition, the effects of velocity dependence on the response of the isolated system are also investigated. Moreover, a parametric study is carried out to critically examine the influence of important parameters on bi-directional interaction effects of the frictional forces of the VFPI. These parameters are: the superstructure time period, frequency variation factor (FVF) and friction coefficient of the VFPI. From the above investigations, it is observed that the dependence of the friction coefficient on relative velocity of the system does not have a noticeable effect on the peak response of the system isolated with VFPI, and that the bi-directional interaction of frictional forces of the VFPI is important and if neglected, isolator displacements will be underestimated and the superstructure acceleration and base shear will be overestimated.

Behavior of Torsionally Coupled Structures with Variable Frequency Pendulum Isolator

The essential characteristics of an effective base isolation system are isolation, energy dissipation, and restoring mechanism. Some friction type base isolation systems proposed earlier have been found to be very effective in reducing the structural response and incorporate simple restoring mechanisms through gravity. However these isolators are effective only under certain excitation and structural characteristics. To overcome these limitations the authors have recently developed a new isolation system called the variable frequency pendulum isolator (VFPI) that has been found to be very effective under a variety of structure and excitation characteristics. In this paper, the mathematical formulation for the three dimensional behavior of an asymmetric structure isolated by a sliding type isolator, with particular reference to VFPI has been presented. The behavior of torsionally coupled structure isolated by VFPI has been examined. The factors affecting the torsional coupling of isolated structure have be...

Aseismic design of structure–equipment systems using variable frequency pendulum isolator

Sliding isolation systems have emerged as very useful vibration control technique that incorporate isolation, energy dissipation and restoring mechanism in one unit. However, most currently available systems such as friction pendulum system (FPS) and pure friction (PF) system have practical limitations and are of limited effectiveness when input excitation level is significantly different from its design level. To overcome these limitations while preserving the advantages, a new system called the variable frequency pendulum isolator (VFPI) has been developed by the authors. The isolation period of VFPI continuously decreases with increase in horizontal sliding displacement which results in a more robust isolation system. The VFPI also limits the maximum force transmitted to the structure by providing a restoring force-softening mechanism. In this paper, it has been shown that isolating a structure using VFPI is very effective for vibration control of structure–equipment and other primary–secondary systems. An example five-storey structure with equipment mounted at its top has been analysed to demonstrate the effectiveness of VFPI. It is shown that VFPI provides better vibration control properties compared to other friction isolation systems, and excellent response reduction is observed for a wide range of equipment properties and excitation characteristics . The performance of the example structure with VFPI has been compared with the other frictional systems such as FPS and PF system.

Earthquake Resistant Design of Structures using the Variable Frequency Pendulum Isolator

The essential properties of sliding isolators used for earthquake resistant design are period shift, energy dissipation, and the restoring mechanism. Isolation systems using a curved surface incorporate all of these in a single unit. The systems currently available have limitations due to their period and restoring force characteristics. The writers have recently proposed a new isolator called the variable frequency pendulum isolator (VFPI), which overcomes theses limitations while retaining the advantages. The oscillation frequency of the VFPI continuously decreases with increase in sliding displacement, and the restoring force has an upper bound so that the force transmitted to the structure is bounded. The mathematical formulation for the response of multi-degree-of-freedom (MDOF) structures isolated using the VFPI has been discussed in this paper. Parametric studies have been carried out to examine the behavior of MDOF structures and structure-equipment systems isolated with the VFPI, friction pendulum system, and pure friction isolator. The VFPI performance is found to be effective and stable during low- and medium-intensity excitations, and fail-safe during high-intensity excitations. The VFPI is also found to exhibit robust performance for a wide range of isolator and ground motion characteristics, clearly demonstrating its advantages for vibration control of MDOF structures.

VFPI: an isolation device for aseismic design

Sliding isolators with curved surface are effective base isolation systems incorporating isolation, energy dissipation and restoring mechanism in one unit. However, practical utility of these systems, such as friction pendulum system (FPS) has limitations due to constant isolator period and restoring force characteristics. A new isolator called the variable frequency pendulum isolator (VFPI) that overcomes these limitations while retaining all the advantages has been described in this paper. VFPI has oscillation frequency decreasing with sliding displacement, and the restoring force has an upper bound so that the force transmitted to the structure is limited. The mathematical formulations for the response of a SDOF structure and energy balance are also described. Parametric studies have been carried out to critically examine the behaviour of structures isolated with VFPI, FPS and PF system. From these investigations, it is concluded that the VFPI combines the advantages of both FPS and PF system, without their undesirable properties. The VFPI performance is also found to be stable during low-intensity excitations, and fail-safe during high-intensity excitations. VFPI is found to exhibit robust performance for a wide range of structure, isolator and ground motion characteristics clearly demonstrating its advantages. Copyright © 2000 John Wiley & Sons, Ltd.