Moments of Nonlinear Systems

by Mario Di Paola, Dipartimento di Ingegneria, Strutturale e Geotecnica, Italy,

Document Type: Proceeding Paper

Part of: Probabilistic Methods in Civil Engineering


In this paper the problem of writing the equations of moments of nonlinear systems excited by both external and parametric Gaussian white processes is re-examined. The classical K. Ito approach gives the equations in terms of moments one at a time not revealing a fully clear mathematical structure of these equations. Here, using the tensor product to define the moments of a fixed order of the response vector, a new procedure is presented for deriving differential equations of moments in compact and repetitive form.

Subject Headings: Nonlinear response | Nonlinear analysis | Moment (mechanics) | Differential equations | Mathematics | Gaussian process | Equations of motion

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