Investigation of transverse galloping in the presence of structural nonlinearities: theory and experiment
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ORIGINAL PAPER
Investigation of transverse galloping in the presence of structural nonlinearities: theory and experiment Shimon Regev · Oriel Shoshani
Received: 19 May 2020 / Accepted: 13 October 2020 © Springer Nature B.V. 2020
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 ringdown 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 S. Regev · O. Shoshani (B) Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel e-mail: [email protected] S. Regev e-mail: [email protected]
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. Keywords Aeroelasticity · Flow-induced vibration · Transverse galloping · Self-sustained oscillations
1 Introduction When a bluff viscoelastic structure is immersed in an airstream above a certain airflow velocity, it can experience aeroelastic transverse galloping instability due to the nonlinear interaction between the unstable wake of the bluff structure and a degree of freedom of the viscoelastic structure that is transverse to the direction of the flow. At the instability threshold, the added linear damping from the airflow changes sign—from positive to negative—such that the airflow changes roles: from being an energy sink that dissipates the energy of the structure, to being an energy source that pumps energy to the structure. The oscillatory nature of the transverse galloping instability increases the amplitude of the transverse motion until nonlinear effects commence and the amplitude saturates at a stable limit cycle. While most researchers try to avoid transverse galloping instabilities due to their potentially catastrophic effect on engineering structures [1–5],
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