doi:10.3850/978-981-08-7619-7_P040

ABSTRACT

A new technique is presented for determining the response moments of systems subject to random excitations. The technique can be construed as the moment evolution version of the so-called probability density evolution equation (PDEE) technique. In its implemention, ordinary differential equations (ODE) are used to determine the moments of response, vis a vis the PDEE partial differential equations (PDE) which must be solved to determine the probability density functions (PDFs) of the response. Similarly to the procedure of PDEE, the moment evolution equation requires sample velocity responses with certain preassigned probabilities. These sample velocities are obtained herein by exciting systems by corresponding sample excitations whose ensemble power spectral density (PSD) is compatible with a target PSD. These sample excitations are synthesized by using the stochastic harmonic function (SHF) representation. This representation is, in certain respects, similar to the spectral representation, but the random terms used in the former include not only random phases but also random frequencies. The proposed technique is used in calculating the moment evolution of the response of a Duffing oscillator, subjected to limited-band white noise, to random excitation with Kanai-Tajimi spectrum, and to separable non-stationary random process. Comparisons with the results from a pertinent Monte Carlo simulation support the reliability of the technique.

Keywords: Moment evolution, Stochastic harmonic function, Monte Carlo simulation, Probability density evolution equation (PDEE), Uniformly distributed sequence.

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