Random vibration and reliability analysis of fluid-conveying pipe under white noise excitations

Due to the random excitation in the external environment, the fluid-conveying pipe would inevitably undergo random vibration. This paper investigates the random vibration and reliability of simply-supported fluid-conveying pipes under white noise excitations. Dynamic equations of the nonlinear pipe conveying fluid under white noise excitations are modeled by the generalized Hamilton principle. Then probability density functions (PDFs) of the amplitude and energy of the system are determined by using the modified stochastic averaging method. The PDFs of displacement and velocity of the system are also discussed. The accuracy of results is verified by the Monte Carlo method. In addition, the first-passage problem of the pipe system is investigated for the first time. In order to obtain the PDFs of reliability and first failure time of the system, the forward finite difference method is adopted to solve the backward Kolmogorov equation of the system. The effects of different parameters on the amplitude, energy, reliability, and first failure time are investigated. The results show that the amplitude of the system becomes large and the first-passage time is advanced with the increase of excitation intensity or fluid speed. The amplitude of the system is decreased and the first-passage time is delayed with the increase of the damping coefficient.