Stochastic linearization method with random parameters for SDOF nonlinear dynamical systems: Prediction and identification procedures

This paper describes firstly, the calculation of the Power Spectral Density Function (PSDF) for the stationary response of SDOF nonlinear second-order dynamical systems excited by a white or a broad-band Gaussian noise, and secondly, the identification of a single-degree-of-freedom (SDOF) nonlinear dynamical second-order dynamical system driven by a broad-band or a colored Gaussian noise. The two aspects are based on the use of a stochastic linearization method with random parameters which is an efficient way of approximating the PSDF. The gain obtained by this method is shown on a SDOF nonlinear dynamical system. In addition, it is shown that the stochastic linearization method with random parameters is an efficient approach for identifying a SDOF nonlinear dynamical system.

[1]  R. Roy.  Stochastic averaging of oscillators excited by colored Gaussian processes , 1994 .

[2]  R. G. Medhurst,et al.  Topics in the Theory of Random Noise , 1969 .

[3]  Helmut J. Pradlwarter,et al.  Equivalent linearization (EQL) in engineering practice for aseismic design , 1994 .

[4]  R. Bouc.  The Power Spectral Density Of Response For A Strongly Non-linear Random Oscillator , 1994 .

[5]  Frank Kozin,et al.  Structural parameter identification techniques , 1988 .

[6]  W. D. Iwan,et al.  Response Envelope Statistics for Nonlinear Oscillators With Random Excitation , 1978 .

[7]  Isaac Elishakoff,et al.  Approximate solution for nonlinear random vibration problems by partial stochastic linearization , 1993 .

[8]  R. Val Ery Roy.  Stochastic Averaging of Oscillators Excited by Colored Gaussian Processes , 1994 .

[9]  Yu-Kweng Michael Lin.  Probabilistic Theory of Structural Dynamics , 1976 .

[10]  P. Spanos,et al.  Stochastic averaging: An approximate method of solving random vibration problems , 1986 .

[11]  J. Bendat.  New techniques for nonlinear system analysis and identification from random data , 1990 .

[12]  Y. K. Lin,et al.  Some observations on the stochastic averaging method , 1986 .

[13]  Ronald N. Miles.  An approximate solution for the spectral response of Duffing's oscillator with random input , 1989 .

[14]  On improved stochastic averaging procedure , 1994 .

[15]  Masanobu Shinozuka,et al.  Simulation of Multivariate and Multidimensional Random Processes , 1971 .

[16]  Christian Soize,et al.  The Fokker-Planck Equation for Stochastic Dynamical Systems and Its Explicit Steady State Solutions , 1994, Series on Advances in Mathematics for Applied Sciences.

[17]  P. Spanos,et al.  Random vibration and statistical linearization , 1990 .

[18]  P. Spanos,et al.  Stochastic Linearization in Structural Dynamics , 1988 .

[19]  W. Schiehlen,et al.  on Analysis and estimation of stochastic mechanical systems , 1988 .

[20]  Masanobu Shinozuka,et al.  Structural Safety and Reliability , 2000 .

[21]  J. B. Roberts.  The energy envolope of a randomly excited non-linear oscillator , 1978 .

[22]  T. Caughey.  Equivalent Linearization Techniques , 1962 .