Nonlinear mathematical model of unsteady galloping force on a rectangular 2:1 cylinder

This paper aims at establishing a reliable mathematical model for unsteady galloping instability or the combined effects of VIV and galloping. Instead of only basing on galloping displacement, the unsteady galloping force (UGF) is measured directly from spring-suspended sectional model tests through an improved force measurement technique. The measured UGF is found to be able to numerically reconstitute the galloping displacement responses with acceptable accuracy. In establishing an UGF model from the measured force, an energy equivalent principle (EEP) is proposed to simplify the modeling procedure and identifying aerodynamic parameters. The obtained UGF force model contains a third-order and fifth-order velocity terms to consider aerodynamic damping nonlinearities, and the unsteady effect of galloping is modeled by considering the variation of aerodynamic parameters with reduced wind speed. It is found that the negative aerodynamic damping provided by the first-order and third-order velocity terms is the source of the power driving the development of the unsteady galloping, while the positive aerodynamic damping provided by the fifth-order velocity term acts as a stabilizer making the galloping amplitude stable finally. The effectiveness of proposed UGF model and EEP in parameters identification was validated by comparing the numerically calculated galloping amplitude with experimental results.