Stochastic Stability of a Pipeline Affected by Pulsate Fluid Flow

Discussion on Stochastic Analysis of Hydraulic Vibration in Pressurized Water Diversion and Hydropower Systems

“…Equations (17) and (18) are typical first-order and second-order inhomogeneous ordinary differential equations, respectively. Given known f 0 (t) and f i (t), it is easy to derive the deterministic solutions of q 0 and oscillating flow rate q i (i = 1, 2, .…”

“…The dynamic interaction between the unsteady flow occurrence and the resulting vibration of the pipe was analyzed based on experiments and numerical models, and the importance of integrated analysis of fluid-structure interaction was then emphasized [17]. Based on the assumption of Poisson characteristics and application of stochastic modification of the second Lyapunov method for the pulsating fluid flow, the stability conditions of a pipeline section were analyzed [18]. Wu et al [19] and Ohashi [20] comprehensively introduced the vibration and oscillation problems hazardous to the safety and reliable operation of hydraulic machinery and the problems caused by mechanical or hydraulic excitation, including self-excited vibration, along with the possible operational instability of the hydraulic, mechanical, structural, and power systems.…”

On Stability of Pin-Jointed Beam Affected by Random Pulsating Load

“…then for any initial condition r r ( ) 0 0 = the solution of equation (28) tends to zero with probability one (Carkovs and Stoyanov, 2005). To find a solution of equation 34we apply the algorithm proposed by Carkovs and Matvejevs (2015). We will look for the solution of this equation as a singular at the point e = 0 function…”