Explicit closed-form solutions of the initiation conditions for 3DOF galloping or flutter

Abstract

The initial conditions of wind-excited multiple degrees of freedom bridge flutter or transmission conductor galloping are often determined through a numerical complex eigenvalue analysis in which one of the modal damping becomes negative. This study presents explicit closed-form solutions of the complex eigenvalue problem in terms of modal frequencies, damping ratios and coupled motions of three degrees of freedom (3DOF) systems influenced by self-excited aerodynamic forces. The framework is first developed for 3DOF coupled bridge flutter considering the fundamental vertical, lateral and torsional modes. It is then applied to 3DOF galloping of ice-accreted transmission conductors where the self-excited forces are modeled from linearization of quasi-steady theory, and the structural coupling resulted from the eccentricities of mass and rigidity are also considered. The general solutions shed clear insights on the influence of aerodynamic force coefficients, structural dynamic parameters and eccentricities on the galloping instability. The accuracy of the proposed solutions is demonstrated using a four-bundled transmission conductor. The generation mechanism of various galloping vibrations with different coupled motions is clarified. The influences on the galloping conditions of ice position, wind direction, structural dynamic parameters and eccentricities as well the modeling of aerodynamic forces induced by torsional velocity of motion are examined.