Random vibration and first-passage of a pipe conveying fluid under colored noise excitations

Colored noise characterized by correlated time dependence is frequently encountered in practical engineering applications. This study investigates the random responses, reliability, and first-passage time of a fluid-conveying pipe subjected to colored noise excitations. The governing equation of the fluid-conveying pipe system excited by colored noise is derived based on the Hamilton principle. Subsequently, the probability density function (PDF) of the steady-state responses for the fluid-conveying pipe is calculated through the modified stochastic average method. The effectiveness of the analysis results is verified through the Monte Carlo method. Additionally, PDFs of reliability and first-passage time are obtained by solving the backward Kolmogorov equation using the finite difference approach. The influences of fluid speed, noise intensity as well as filter factor on the dynamic behavior of the system are discussed. Specifically, their effects on the PDFs with amplitude and energy for dynamic characteristics, as well as on reliability and the first-passage time are analyzed. The results indicate that the increasing fluid speed leads to greater maximum displacement, larger total energy, decreased reliability, and earlier first-passage time for the pipe system. Conversely, an increase in the filter coefficient causes the greater maximum displacement, decreased total energy, improved dynamic reliability, and delayed first-passage time for the pipe system. These findings provide valuable insights into the design and operation of pipe systems under colored noise excitations.