Dynamic Analysis of Bilinear Oscillators Excited by Band-limited White Noise Excitation

Document Type : Research Note

Authors

University of Kurdistan

Abstract

The response spectrum of an oscillator with bilinear stiffness excited by band-limited Gaussian white noise is considered. The response is obtained by integrating over all energy levels weighting each with the stationary probability density of the energy. The procedure presented leads to estimates of linear and nonlinear response spectra in frequency domain and agrees well with those obtained by direct numerical simulation. Development of stochastic-based response spectra based on the frequency information concerning ground motions is important in engineering. Approximation of non-stationary ground motions by band-limited white noise is shown to be adequate for systems at the structural periods of engineering interest. Formulating the nonlinear response based on the excitation frequency information opens a door for wider use of seismological theory for regions with scarcely available recorded ground motion data. Despite simplicity and computational efficiency of the method, it provides an accurate prediction of the observed nonlinear response spectra on average.

Keywords

References

Rudinger, F. and Krenk S. (2003) Spectral density of oscillator with bilinear stiffness and white noise excitation. Probabilistic Engineering Mechanics, 18, 215-222.
Koliopulos, P.K. and Nichol, E.A. (1994) Comparative performance of equivalent linearization techniques for inelastic seismic design. Engineering Structures, 16(1), 5-10.
Crandall, S.H. (1963) Perturbation techniques for random vibration of nonlinear systems. J. Acoust. Soc. Am., 35, 1700-1705.
Caughey, T.K. (1971) Nonlinear Theory of Random Vibrations, Advances in Applied Mechanics. New York: Academic Press, 209-253.
Roberts, J.B. and Spanos, P.T.D. (1986) Stochastic averaging: An approximate method of solving random vibration problems. Int. J. Nonlinear Mech., 21, 111-134.
Dimentberg, M.F. (1996) Random vibrations of an isochronous SDOF bilinear system. Nonlinear Dynamics, 11, 401-405.
Iourtchenko, D.V. and Song, L.L. (2006) Numerical investigation of a response probability density functions of stochastic vibroimpact systems with inelastic impacts. International Journal of Non-Linear Mechanics, 41, 447-455.
Manohar, C.S. (1995) Methods of nonlinear random vibration analysis. Sadhana , 20, 345-371.
Miles, R. (1989) An approximation solution for spectral response of Duffing's oscillator with random input. Journal of Sound and Vibration, 132, 43-49.
Bellizzi, S. and Bouc, R. (1996) Spectral response of asymmetrical random oscillators. Probabilistic Engineering Mechanics, 11(5), 1-9.
Lin, Y.K. and Ca, G.Q. (1988) Exact stationary response solution for second order nonlinear systems under parametric and external white noise excitations: Part II. Journal of Applied Mechanics, 55, 702-705.
Lin, Y.K. and Cai, G.Q. (2004) Probabilistic Structural Dynamics: Advanced Theory and Applications. McGraw-Hill, New York, 546p.
Cai, G.Q. and Lin, Y.K. (1997) Response spectral densities of strongly nonlinear systems under random excitation. Probabilistic Engineering Mechanics, 12, 41-47.
Yazdani, A. and Salimi, M-R. (2015) Earthquake response spectra estimation of bilinear hysteretic systems using random-vibration theory method. Earthquakes and Structures, 8(5), 1055-1067.
Yazdani, A. and Komachi, Y. (2009) Computation of earthquake response via fourier amplitude spectra. International Journal of Engineering, 22(2), 147-152.
Yazdani, A. and Takada, T. (2011) Probabilistic study of the influence of ground motion variables on response spectra. Structural Engineering and Mechanics, 39(6), 877-893.
Zhu, W.Q., Haung, Z.L., and Suzuki, Y. (2001) Response and stability of strongly nonlinear oscillators under wide-band random excitation. Int. J. Nonlinear Mech., 36, 1235-1250.
Kumar, D. and Datta, T.K. (2006) Stochastic response of nonlinear system in probability domain. Sadhana, 31(4), 325-342.
Huai, X., Xianren, K., Zhenguo, Y., and Yuan, L. (2015) Response regimes of narrow-band stochastic excited linear oscillator coupled to nonlinear energy sink. Chinese Journal of Aeronautics, 28(2), 457-468.
Caughey, T.K. (1986) On the response of nonlinear oscillators to stochastic excitation. Probabilistic Engineering Mechanics, 1, 2-10.
Krenk, S. and Roberts, J.B. (1999) Local similarity in non-linear random vibration. Journal of Applied Mechanics, 66, 225-235.
Takewaki, I. (2001) Resonance and criticality measure of ground motions via probabilistic critical excitation method. Soil Dynamic and Earthquake Engineering, 21, 645-659.
Brune, J.N. (1970) Tectonic stress and the spectra of seismic shear waves from earthquakes. Journal of Geophysical Research, 75, 4997-5009.
Boore, D.M. (2003) Prediction of ground motion using the stochastic method. Pure Appl. Geophys., 160, 35-676.
Kanamori, H. (1977) The energy release in great earthquakes. J. Geophys Res., 82, 2981-2987.
Anderson, J.G. and Hough, S. (1984) A model for the Fourier amplitude spectrum of acceleration at high frequency. Bull. Seismol. Soc. Am., 74(5), 1969-1993.
Boore, D.M. and Joyner, W.B. (1997) Site amplification for generic rock sites. Bull. Seismol. Soc. Am., 87(2), 327-341.
Boore, D.M. (2009) Comparing stochastic point-source and finite-source ground-motion simulations: SMSIM and EXSIM. Bull. Seismol. Soc. Am., 99(6), 3202-3216.
Atkinson, G.M. and Silva, W. (2000) Stochastic modeling of California ground motions. Bull. Seismol. Soc. Am., 90, 255-274.
Atkinson, G.M. and Boore, D.M. (1995) Ground motion relations for eastern North America. Bull. Seismol. Soc. Am., 85, 17-30.
Journal of Seismology and Earthquake Engineering
Volume 17, Issue 3 - Serial Number 3
Autumn 2015
Pages 213-222

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