Non-stationary response autocorrelation function of nonlinear oscillators endowed with fractional derivative elements

Abstract

An approximate analytical technique is developed for determining the non-stationary response autocorrelation function of nonlinear oscillators endowed with fractional derivative elements. Specifically, first, a stochastic averaging/linearization treatment is employed [1] for deriving an input-output relationship in the joint time-frequency domain. The derived relationship between the excitation and the response evolutionary power spectra (EPS) can be construed as an extension of earlier results in the literature [2] to account for fractional derivative elements in the oscillator equation of motion. Further, the non-stationary response autocorrelation function can be readily determined based on an approximate approach proposed in [3]. A nonlinear oscillator with fractional derivative elements and subjected to non-stationary stochastic excitation with an EPS is considered as a numerical example. The reliability of the developed technique is demonstrated by comparisons with pertinent Monte Carlo simulation data.

REFERENCES

[1] Fragkoulis, V. C., Kougioumtzoglou, I. A., Pantelous, A. A. and Beer, M., 2019. Non-stationary response statistics of nonlinear oscillators with fractional derivative elements under evolutionary stochastic excitation. Nonlinear Dynamics, 97(4), 2291-2303.

[2] Kougioumtzoglou, I. A., 2013. Stochastic joint timeﾖfrequency response analysis of nonlinear structural systems. Journal of sound and Vibration, 332, 7153-7173.

[3] Benowitz, B. A., Shields, M. D., Deodatis, G., 2015. Determining evolutionary spectra from non-stationary autocorrelation functions. Probabilistic Engineering Mechanics, 41, 73-78.