Earthquake Barcode from a Single-Degree-of-Freedom System


Earthquake is a violent and irregular ground motion that can severely damage structures. In this paper we subject a single-degree-of-freedom system, consisting of spring and damper, to an earthquake excitation, and meanwhile investigate the response behavior from a novel theory about the dynamical system, by viewing the time-varying signum function of It can reflect the characteristic property of each earthquake through and the second component of f, where is a time-sampling record of the acceleration of a ground motion. The barcode is formed by plotting with respect to time. We analyze the complex jumping behavior in a barcode and an essential property of a high percentage occupation of the first set of dis-connectivity in the barcode from four strong earthquake records: 1940 El Centro earthquake, 1989 Loma earthquake, and two records of 1999 Chi-Chi earthquake. Through the comparisons of four earthquakes, we can observe that strong earthquake leads to large percentage of the first set of dis-connectivity.

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Liu, C. and Chang, C. (2015) Earthquake Barcode from a Single-Degree-of-Freedom System. Natural Science, 7, 18-31. doi: 10.4236/ns.2015.71003.

Conflicts of Interest

The authors declare no conflicts of interest.


[1] Loh, C.H., Lee, Z.K., Wu, T.C. and Peng, S.Y. (2000) Ground Motion Characteristics of the Chi-Chi Earthquake of 21 September 1999. Earthquake Engineering and Structural Dynamics, 29, 867-897.<867::AID-EQE943>3.0.CO;2-E
[2] Sokolov, V.Y., Loh, C.H. and Wen, K.L. (2002) Comparison of the Taiwan Chi-Chi Earthquake Strong-Motion Data and Ground-Motion Assessment Based on Spectral Model from Smaller Earthquakes in Taiwan. Bulletin of the Seismological Society of America, 92, 1855-1877.
[3] Sokolov, V.Y., Loh, C.H. and Wen, K.L. (2003) Evaluation of Hard Rock Spectral Models for the Taiwan Region on the Basis of the 1999 Chi-Chi Earthquake Data. Soil Dynamics and Earthquake Engineering, 23, 715-735.
[4] Chopra, A.K. (1995) Dynamics of Structures: Theory and Applications to Earthquake Engineering. Prentice-Hall, New Jersey.
[5] Kramer, S.L. (1996) Geotechnical Earthquake Engineering. Prentice-Hall, New Jersey.
[6] Kanai, K. (1957) Semi-Empirical Formula for the Seismic Characteristics of the Ground. Bulletin of the Earthquake Research Institute, University of Tokyo, 35, 309-325.
[7] Tajimi, H. (1960) A Statistical Method of Determining the Maximum Responses of a Building Structure during an Earthquake. Proceeding of the 2nd World Conference on Earthquake Engineering, Japan, 781-797.
[8] Liu, C.-S. (2001) Cone of Non-Linear Dynamical System and Group Preserving Schemes. International Journal of Non-Linear Mechanics, 36, 1047-1068.
[9] Liu, C.-S. and Jhao, W.S. (2014) The Second Lie-Group SOo(n,1) Used to Solve Ordinary Differential Equations. Journal of Mathematic Research, 6, 18-37.
[10] Liu, C.-S. (2014) Disclosing the Complexity of Nonlinear Ship Rolling and Duffing Oscillators by a Signum Function. CMES: Computer Modeling in Engineering & Sciences, 98, 375-407.
[11] Liu, C.-S. (2015) A Novel Lie-Group Theory and Complexity of Nonlinear Dynamical Systems. Communications in Nonlinear Science and Numerical Simulation, 20, 39-58.

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