Flow-Induced Vibration Of Pipes In Cross And Internal Flow

This thesis examines the dynamics of pipe system in internal and cross flow. Using force balance method, the nonlinear equations of motion are derived for cantilevered pipes. Galerkin’s Method and DQ Method are proposed to analyze this pipe model. Particular attention is concentrated on the stability boundary in linear pipe system and bifurcation routs&chaotic motions in non-linear system. In contrast to the works by other investigators, the present thesis represents several features as follows:1. Base on the engineering problem, the motion equations of pipe system in internal and cross flow are derived with force balance method. Complex elastic support at both ends is consider to be the boundary condition. In non-linear system, the cantilevered pipe supported by a cubic spring is analyzed.2. The linear system is first studied. Depending on the internal flow velocity is constant or not, two kinds of linear systems are investigated:constant internal flow and oscillatory internal flow. And the emphasis is put on the system parameters’effect on the stability boundary and kinds of instabilities. In the case of oscillatory internal flow, the direct multi-scale method is proposed in numerical simulation of parametric resonance.3. As the analyze in linear system, the nonlinear system is also separated in two parts by the internal flow velocity. In each part, three cases are considered:the pipe in only the internal flow, the forced vibration of the pipe in internal flow and finally the pipe in both internal flow and the outside cross flow. With the comparison of these three cases in each part and by means of the bifurcation diagram, phase portraits of the motion and PSD diagram, the effect of parameter variation on pipe vibration is investigated. Bifurcation and the routs to chaos are of considerable interest.