Dynamic Behavior and Sensitivity Analysis for Structural Systems with Longitudinal Mass Flow

Abstract

The dynamic behaviors of the structural systems with longitudinal mass flow are very important from engineering points of view. However, they have not been studied so detailly, especially in general manners for various structures with different boundary conditions. In this study, structural systems with longitudinal mass flow were considered as flexible moving beams in longitudinal direction, and the flexible moving beams were taken as the longitudinal mass flow inside the idealized massless pipes with the same rigidity of the beams and a method of dynamic analysis was derived. And complex eigenvalue analysis and dynamic stability analysis of non-cyclic and cyclic structural systems were held by following the dynamic analysis method and considerations on dynamic behaviors and stability were taken for various boundary conditions from view points of energy and property matrices etc. It is known that the dynamic stabilities mainly depend upon such parameters as mass fiow's velocities, tensions, elastic modulus and cross sectional areas etc. A method of sensitivity analysis of complex eigenvalues with respect to such parameters was also presented here. Then we showed an application of the sensitivities which may extend the stable areas. Based on the presented methods, numerical examples of complex eigenvalues and sensitivities are obtained and examined and the applications of the sensitivities are also discussed to show the effectiveness of the method.