An efficient stochastic natural frequency analysis method for axially varying functionally graded material pipe conveying fluid

Abstract

This study proposes an effective approach for stochastic natural frequency analysis of axially varying functionally graded material (FGM) pipes conveying fluid. The Karhunen-Loève expansion is first employed to generate a random filed with axially varying FGM properties. Then the input uncertainty is substituted into the governing equation of axially varying FGM pipes conveying fluid. The stochastic differential quadrature method is introduced to derive the generalized eigenvalue equation and obtain the natural frequencies. Based on the established stochastic mechanical model, the statistical characteristics of the stochastic natural frequency response can be estimated. In order to mitigate the calls of the mechanical model, a Kriging model requiring a rather small design of experiment is utilized to mimic the true mechanical model. An approach combining the material random field, the derived generalized eigenvalue equation and the Kriging model is finally proposed. The example investigations have validated the effectiveness as well as the efficiency of the proposed strategy for stochastic natural frequency analysis of axially varying FGM pipes conveying fluid with random material properties.