Stochastic natural frequency analysis of varying diameter functionally graded material pipe conveying fluid

Abstract

This paper investigates the uncertainty of the structure and material parameters on the natural frequency of the varying diameter functionally graded material (FGM) pipe conveying fluid. Firstly, concentrating on the spatially dependent uncertainty of geometry varying in axial direction as well as the material varying in radial direction, the random field is employed to describe the uncertainty parameters. Then, a generalized eigenvalue equation of the varying diameter FGM pipe is derived by the dynamic stiffness method while introducing the random field and variables into the deterministic governing equation. Due to the input uncertainty, the natural frequencies of the varying diameter FGM pipe change to random variables. In this respect, the stochastic characteristics of natural frequencies can be approximated by the Monte Carlo simulation. However, the enormous computational cost is unbearable. The efficient artificial neural network surrogate model is introduced and incorporated for the natural frequency uncertainty quantification. Consequently, a stochastic natural frequency analysis approach based on the neural network is proposed for the varying diameter FGM pipe conveying fluid. Some examples are investigated to illustrate the effectiveness of the proposed method and the influence of input uncertainty on the probabilistic characterization of the natural frequencies.