Stochastic linearization of systems with hysteretic characteristics

Authors

  • Ovidiu Solomon
  • Ana Maria Mitu
  • Marius Giuclea

Keywords:

stochastic linearization, hysteretic characteristic, random excitation, Bouc-Wen model

Abstract

In this paper is presented a linearization method for a stochastic differential system with hysteretic characteristics and random excitation. The Gaussian equivalent linearization technique is applied to a system with hysteretic characteristic modeled by a Bouc-Wen equation. In order to verify the efficiency of the linearization method, the standard deviations of the equivalent linear system response are compared with those of Bouc-Wen nonlinear system for two case studies: Gaussian white noise and seismic inputs.

References

BOUC, R., Forced vibration of mechanical systems with hysteresis, Proceedings of the Fourth Conference on Nonlinear oscillation, Prague, Czechoslovakia, 1967.

WEN, Y.K., Method for random vibration of hysteretic systems, Journal of the Engineering Mechanics Division, 102, 2, pp. 249–263, 1978.

DOBSON, S., NOORI, M., HOU, Z., DIMENTBERG, M., BABER, T., Modelling and random vibration analysis of SDOF systems with asymmetric hysteresis, International Journal of NonLinear Mechanics, 32, 4, pp. 669–680, 1997.

HURTADO, J.E., BARBAT, A.H., Equivalent linearization of the Bouc-Wen hysteretic model, Engineering Structures, 22, 9, pp. 1121–1132, 2000.

ROBERTS, J.B., SPANOS, P.D., Random vibration and statistical linearization, John Wiley and Sons, 1990.

KRYLOV, N., BOGOLIUBOV, N., Introduction to nonlinear mechanics, Princeton University Press, New York, 1943.

CAUGHEY, T.K., Equivalent linearization techniques, J Acoustical Soc Am, 35, 11, pp. 1706– 1711, 1963.

IWAN, W.D., A generalization of the concept of equivalent linearization, Int. J. Nonlinear Mech., 8, 3, pp. 279–287, 1973.

ATALIK, T.S., UTKU, S., Stochastic linearization of multi-degree of freedom non-linear systems, Earthquake Engineering & Structural Dynamics, 4, 4, pp. 411–420, 1976.

FARAVELLI, L., CASCIATI, F., SINGH, M.P., Stochastic equivalent linearization algorithms and their applicability to hysteretic systems, Meccanica, 23, 2, pp. 107–112, 1988.

SPANOS, P-T.D., IWAN, W.D., On the existence and uniqueness of solution generated by equivalent linearization, Int. J. Non-Linear Mech., 13, 2, pp. 71–78, 1978.

BOUC, R., Forced vibration of mechanical systems with hysteresis, Proceedings of the Fourth Conference on Nonlinear Oscillation, Prague, 1967.

WEN, Y.K., Approximate method for nonlinear random vibration, Journal of the Engineering Mechanics Division (ASCE), 101, 4, pp. 389–401, 1975.

BABER, T.T., WEN Y.K., Random vibration of hysteretic, degrading systems, Journal of the Engineering Mechanics Division, 107, 6, pp. 1069–1087, 1981.

Published

2014-10-01