Flow induced vibration of bluff structures

Abstract

Models are developed for both multi-degree-of-freedom aerodynamic galloping and vortex induced oscillation of bluff structures. These models are useful in the analysis of elastic structures exposed to a steady fluid flow. An asymptotic method, based on the approximation of Bogoliubov and Mitropolsky, is developed for the analysis of the autonomous, internally resonant, nonlinear differential equations produced by the models. It is shown that the solutions of these systems can be divided into two classes by the nature of the secular terms arising in the perturbation equations. A model for multi-degree-of-freedom galloping is developed by modeling the aerodynamic forces on the structure as dependent only on the relative magnitude and velocity of the flow to the structure. A simple criterion for the stability of the zero solution is presented. Examples are made with a noninertially coupled system with the torsion and plunge degrees-of-freedom and a cubic curve fit to the aerodynamic coefficients. Examples show that the system is dorninated by either a torsion or a plunge mode except when the natural frequencies of these modes are in certain integer multiples. In these cases the two modes interact strongly and they achieve first order limit cycles simultaneously. A model for vortex induced vibration of elastic structures is produced from a control volume approach to the vortex shedding process. The model features both fluid and structural oscillators. The model parameters are determined from experimental data by matching the model response to experimental observation for the cases of fixed and forced cylinder motion. A frequency entrainment effect is produced by the model for an elastically mounted cylinder resonating with vortex shedding. The resonant amplitude of an elastically mounted cylinder predicted by the model is in good agreement with experimental data.

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