STOCHASTIC DYNAMIC RESPONSE ANALYSIS OF PIPE CONVEYING FLUID BASED ON THE PATH INTEGRAL METHOD

The study of pipes conveying fluid under stochastic excitation is of great importance as they are widely used in engineering. To predict the stochastic dynamic response of pipe conveying fluid system under Gaussian white noise excitation, a dynamic model of the nonlinear pipe conveying fluid under Gaussian white noise excitation is established based on the Hamilton’s principle. The Galerkin truncation method is employed to discretize the governing equation of pipes conveying fluid. The probability density function of the displacement and the probability density function of the velocity of the pipe conveying fluid are calculated by the path integral method based on the Gauss-Legendre formula. The results of the Monte Carlo method are compared with the results obtained by the path integral method to verify the accuracy of the path integral method in the calculation of the vibration response of the pipe conveying fluid. The effects of system parameters such as fluid speed, excitation strength and damping coefficient on the probability density function of the displacement and the probability density function of the velocity of the pipe conveying fluid are investigated. The critical fluid speed when the probability density function of displacement for the pipe conveying fluid has a double peak is determined. The results show that the path integral method is effective in calculating the response of the pipe conveying fluid system. The maximum possible displacement of the system will increase and the maximum possible speed will remain unchanged with the increase of fluid speed. The maximum possible displacement and the maximum possible speed of the system will increase with the increase of excitation strength. Increasing the damping coefficient results in that the maximum possible displacement and the maximum possible speed of the system decreases. In addition, it is found that the increase of fluid speed is one of the factors inducing stochastic bifurcation of the pipe conveying fluid.