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.