PDFs of the stochastic non-linear response of MDOF-systems by local statistical linearization

摘要

A novel computational approach called 'Local Statistical Linearization' (LSL) based on statistical equivalent linearization and Gaussian superposition has been introduced recently. The methodology allows to extend the concept of statistical equivalent linearization to proceed from estimates of the second moment properties of the stochastic response to estimates for the non-Gaussian probability distribution. Locally linearized non-linear systems do not have the properties of a linear system but approximate closely the non-linear characteristic of the system. The suggested approach employs the well developed equivalent linearization procedure or Gaussian closure to compute the non-Gaussian distribution of the response of a non-linear system. Since equivalent linearization is applicable for higher dimensions and FE-models, the suggested approach lends itself to providing numerical solutions for higher dimensional cases. In this paper, the computations of probability density functions of non-linear MDOF-systems are discussed. Moreover, the basic methodology is extended to increase the efficiency of the numerical procedure when dealing with non-linear MDOF-systems.