Abstract:

This study investigates the stochastic stability of simply-supported fluid-conveying pipes under multiplicative Gaussian white noise excitations. The high-dimensional coupled stochastic differential equations for the fluid-conveying pipe are established through the generalized Hamilton principle and the Galerkin truncation method. The stochastic averaging method for quasi non-integrable Hamilton systems is used to decouple and reduce the dimension of the high-dimensional coupled pipe system with gyroscopic forces, yielding a one-dimensional Itô stochastic differential equation for the total energy of the pipe. According to the singular boundary classification theory of one-dimensional time-homogeneous diffusion processes, a stochastic stability criterion for the fluid-conveying pipe is proposed. The stability analyses of the time history responses of energy, displacement, and velocity for the pipe system are obtained via the Monte Carlo approach, thereby verifying the effectiveness of the proposed stability criterion in different parameter planes. Furthermore, the effects of system parameters, such as the fluid speed, multiplicative Gaussian white noise intensity, and pipe length, on the stochastic stability domain of the pipe system are discussed. The results indicate that as the fluid speed, the multiplicative Gaussian white noise intensity acting on the first-order mode, or pipe length increases, the stable domain of the system decreases. Conversely, the stable domain of the fluid-conveying pipe system increases as the multiplicative Gaussian white noise intensity acting on the second-order mode, pipe thickness, or Young’s modulus increases. It is worth noting that the appropriate increase in the multiplicative Gaussian white noise intensity acting on the second-order mode contributes to improving the stable domain of system. This method lays a theoretical foundation for the safe and stable operation of fluid-conveying pipes under random vibration.

Key words: fluid-conveying pipe, stochastic stability, multiplicative Gaussian white noise, stochastic averaging method, singular boundary classification theory