Ismail I. Orabi

A functional series expansion method for response analysis of non-linear systems subjected to random excitations

Abstract A Wiener-Hermite functional series expansion method for response analysis of nonlinear systems under random excitations is presented. The formal procedure for the derivation of the deterministic equations governing the Wiener-Hermite kernel functions is described. A singleterm expansion is used to analyze the non-stationary responses of a damped Duffing oscillator subjected to several modulated white noises. An iterative procedure for evaluating the kernel functions and the mean-square responses of the Duffing oscillator is developed. For several values of non-linearity strength and different damping coefficients the non-stationary variances and autocorrelations of the response are obtained. The results are compared with those found by the digital simulations and the existing methods.

Nonstationary earthquake response of a sliding rigid structure

Abstract The transient and nonstationary responses of a rigid structure sliding on its randomly moving foundation are studied. Stationary and nonstationary, white noise and filtered white noise models for earthquake ground acceleration are considered. The method of nonstationary equivalent linearization in conjunction with the moments of the Fokker-Planck equation is used for the response analysis. The root-mean-square slip displacement and slip velocity responses of the structure are calculated for a range of values of parameters. Monte Carlo digital simulations are also performed and the root-mean-square responses are estimated. The predicted results are compared with those obtained from the simulation technique and exact asymptotic solutions and reasonable agreement is observed. For several values of friction coefficient the responses of the structure to the accelerogram of the North-South component of El Centro 1940 earthquake are also studied. The peak responses are evaluated and the results are compared with those obtained from the statistical analysis. It is shown that for a small coefficient of friction considerable slip could occur. A probabilistic risk analysis is also carried out.

Response of structures subjected to horizontal-vertical random earthquake excitations

A single-degree-of-freedom column subjected to horizontal and vertical earthquake excitations is considered. The earthquake ground accelerations are modelled by segments of stationary and nonstationary Gaussian white noise processes. The Fokker-Planck equation governing the transition probability density of the response is described and the associated second moment equations are derived. The transient and nonstationary response statistics for a range of values of parameters are obtained. A Monte-Carlo digital simulation study is also performed. The results are compared with the theoretical findings and good agreement is observed. Particular attention is given to the amplification effect of the vertical ground acceleration. It is shown that the effect of the vertical ground motion is significant when the load ratio is relatively large. Based on the presented statistical analysis, peak velocity responses for a range of natural periods are estimated. The results are compared with the combined horizontal-vertical response spectra of El Centro 1940 earthquake and reasonable agreement is obtained.

Equivalence of single-term Wiener-Hermite and equivalent linearization techniques

Abstract It is shown that when only the first term of the Wiener-Hermite series is considered, the method becomes equivalent to the time-dependent equivalent linearization technique.

An iterative method for non-stationary response analysis of non-linear random systems

Abstract A method for calculating the non-stationary response of non-linear systems subjected to random excitations is formulated. The time-dependent equivalent linear system is considered and an iterative procedure for evaluating the non-stationary mean-square responses is developed. Several examples are presented and applicability of the technique is illustrated.