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.

The seismic response of a flexible multi-storey building isolated with variable friction pendulum system (VFPS) is investigated under normal component of six near-fault ground motions. The VFPS, an advanced friction base isolator, is proposed in this study. The variation of the friction coefficient in VFPS is such that up to a certain value of displacement the frictional force increases and then it decreases with further increase in displacement. Such variation is selected with the criterion that the isolator displacement and building base shear decrease significantly without much alteration to superstructure acceleration under near-fault ground motions. The governing equations of motion of building isolated with VFPS are derived and solved in the incremental form by using Newmark's step-by-step method assuming linear variation of acceleration over small time interval. In order to verify the effectiveness of VFPS, the seismic responses are compared with that of the same building isolated by conventional friction pendulum system (FPS). A parametric study is also carried out to critically examine the behaviour of building isolated with VFPS. The important parameters considered are the number of stories of superstructure, initial time period and isolation period of the VFPS. In addition, the seismic response of building isolated with VFPS under simple cycloidal pulses is also investigated. From the above investigations, it was concluded that the VFPS is quite effective for controlling the seismic response of buildings under near-fault ground motions. Copyright © 2007 John Wiley & Sons, Ltd.

Earthquake response of slender and broad liquid storage steel tanks isolated with variable curvature friction pendulum systems (VCFPSs) is investigated under near-fault motions. The tanks isolated with VCFPS are idealised with three-degrees-of-freedom associated with convective, impulsive and rigid masses. The frictional forces mobilised at the interface of the VCFPS are assumed to be velocity independent. The governing equations of motion of isolated tank are derived and solved in the incremental form using Newmark's method. For comparative study, the seismic response of liquid storage tanks with the VCFPSs is compared with that of same liquid storage tanks isolated using the friction pendulum systems (FPSs). The seismic response of isolated liquid storage tanks is also compared with that of the non-isolated tanks. Further, a parametric study is carried out to critically examine the behaviour of liquid storage tanks isolated with the VCFPSs. The important parameters considered are the friction coefficient of VCFPS, the fundamental period at the centre of the sliding surface of VCFPS and the tank aspect ratio. It is observed that under near-fault ground motions, the VCFPS is quite effective in controlling the seismic response, viz. the base shear, the sloshing displacement and the impulsive displacement, of liquid storage tanks.

The dynamic response of a flexible multi-story structure isolated with the variable friction pendulum system (VFPS) under near-fault ground motions is investigated. The fault normal and parallel components are applied in two perpendicular horizontal directions of the isolated system. The frictional forces mobilized at the interface of the VFPS are assumed to be independent of the relative sliding velocity. The interaction between frictional forces of the VFPS in two horizontal directions is duly considered and the coupled differential equations of motion of the isolated system are solved in the incremental form by using a step-by-step method with iterations. The iterations are required due to the dependence of frictional forces on the response of the system. The response of the system with bi-directional interaction is compared with that without interaction (i.e., independent two-dimensional idealization in two directions) in order to investigate the effects of bi-directional interaction of the frictional forces. A parametric study is also carried out to critically examine the behavior of the structures isolated with the VFPS under bi-directional excitation. The various important parameters considered are: the superstructure time period, the initial time period, and the isolation period of the VFPS. From the above investigations, it is concluded that the VFPS is quite effective for controlling the seismic response of the structures under bi-directional near-fault ground motions. It is also found that the bi-directional interaction of frictional forces has noticeable effects and if these effects are neglected, the isolator displacements will be under predicted and the superstructure accelerations will be over predicted.

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.