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




Wavelet, VFPI, Variable Curvature, Prediction of Responses, Near-Fault ground motions, Low frequency ground motions


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.


Download data is not yet available.

Author Biographies

Harshal Admane, Research Scholar

Harshal A. Admane is a Ph.D. candidate in the Department of Civil Engineering at Government College of Engineering, Aurangabad. He has been joined to this institute under AICTE Doctored Fellowship (ADF) – 2018 program. The primary aim of his research work to provide the simplest way to calculate the response of structure isolated by Variable Frequency Pendulum Isolator (VFPI) and investigate the performance of VFPI experimentally. He has also received funding from AICTE-RPS for conduction of his experimental research work.

Pranesh Murnal, Professor

Pranesh B. Murnal was a professor in the Department of Applied Mechanics at Government College of Engineering Aurangabad and has more than 35 years of experience in industry and academia. He has completed his Ph.D. from Indian Institute of Technology, Bombay. His Ph.D. thesis has got the “Innovative Potential of Student Project Award” at national level conferred by Indian National academy of Engineering, New Delhi for the year 2001. He has a research background in earthquake engineering and structural dynamics and has consulted widely in these fields. He has two patents registered in his name for the invention of a new friction base isolation named as “Variable Frequency Pendulum Isolator (VFPI).


Admane, H. A., and Murnal, P. (2021). “Comparative Analysis of SIVC Systems Using Simplified Analytical Modeling for Practical Design.” Practice Periodical on Structural Design and Construction, 26(1), 04020051. DOI:

Gabor, D. (1946). “Theory of communication. Part 1: The analysis of information.” Journal of the Institution of Electrical Engineers - Part III: Radio and Communication Engineering, 93(26), 429–441. DOI:

Lu, L., Shih, M., and Wu, C. (2004). “Near-Fault Seismic Isolation Using Sliding Bearings With Variable Curvatures.” 13th World Conference on Earthquake Engineering, Vancouver, B.C., Canada, 3264–3278.

Malu, G., and Murnal, P. (2014). “Performance Evaluation of VFPI Subjected Near-Fault Ground Motion Through Wavelet Excitation.” SEC-2014, Bloomsbury Publishing India Pvt Ltd., Delhi, India, 3136–3146.

Mavroeidis, G. P., and Papageorgiou, A. S. (2003). “A mathematical representation of near-fault ground motions.” Bulletin of the Seismological Society of America, 93(3), 1099–1131. DOI:

Murnal, P., and Sinha, R. (2002). “Earthquake Resistant Design of Structures using the Variable Frequency Pendulum Isolator.” Journal of Structural Engineering, 128(7), 870–880. DOI:

Murnal, P., and Sinha, R. (2004). “Behavior of Torsionally Coupled Structures with Variable Frequency Pendulum Isolator.” Journal of Structural Engineering, 130(7), 1041–1054. DOI:

Panchal, V. R., and Jangid, R. S. (2008). “Seismic behavior of variable frequency pendulum isolator.” Earthquake Engineering and Engineering Vibration, 7(2), 193–205. DOI:

Pranesh, M., and Sinha, R. (2000). “VFPI: an isolation device for aseismic design.” Earthquake Engineering & Structural Dynamics, 29(5), 603–627. DOI:<603::AID-EQE927>3.0.CO;2-W

Shaikhzadeh, A. A., and Karamoddin, A. (2016). “Effectiveness of sliding isolators with variable curvature in near-fault ground motions.” The Structural Design of Tall and Special Buildings, 25(6), 278–296. DOI:

Tsai, C. S., Chiang, T. C., and Chen, B. J. (2003). “Finite element formulations and theoretical study for variable curvature friction pendulum system.” Engineering Structures, 25(14), 1719–1730. DOI:

Zayas, V. A., Low, S. S., and Mahin, S. A. (1990). “A Simple Pendulum Technique for Achieving Seismic Isolation.” Earthquake Spectra. DOI:




How to Cite

Admane, H. and Murnal, P. (2022) “Response Prediction of VFPI Through Equivalent Long Period Wavelet of Near-Fault Ground Motion”, Electronic Journal of Structural Engineering, 22(2), pp. 53–67. doi: 10.56748/ejse.222982.