Investigation of transverse galloping in the presence of structural nonlinearities: theory and experiment

Abstract

We formulate and experimentally validate a theoretical reduced-order model for the transverse galloping of nonlinear structures, namely a pair of identical, parallel-oriented cantilever beams whose free ends are attached to square prisms. We derive the structural nonlinearities from (a) a single-mode approximation of the nonlinear (truncated at cubic order) equation of motion, calculated for conservative cantilever beams augmented by a non-conservative aerodynamic force acting on a prism; and (b) phenomenological linear, quadratic, and cubic damping forces. We estimate the coefficients of the damping forces from the ring-down responses of the structures in still air. We analyze the deterministic dynamics of transverse galloping that stem from the aerodynamic force of the quasi-steady theory, and the stochastic effect of spectral line broadening that stem from turbulence-induced random fluctuations. Our findings clearly show that standard nonlinear macroscopic structures exhibit considerably different steady-state response curves than the universal curve of Parkinson obtained for linear mass–spring–damper structures. Importantly, the amplitudes of the oscillations are attenuated at high upstream velocities due to nonlinear damping, while the spectral line broadens due to turbulence-induced random fluctuations and an amplitude-to-phase noise conversion, which lowers the quality of the self-sustained oscillations. These two phenomena should be considered in the design of efficient transverse galloping-based energy harvesters—a rapidly growing field of research.