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.

我们制定并实验验证了非线性结构的横向驰振的理论降阶模型，即一对相同的，平行定向的悬臂梁，其自由端连接到方形棱镜。我们从以下方面得出结构非线性：（a）非线性（以三次阶截断）运动方程的单模近似，该方程是为保守的悬臂梁通过作用在棱镜上的非保守空气动力而计算的；（b）现象学上的线性，二次和三次阻尼力。我们从静止空气中结构的振铃响应估计阻尼力的系数。我们根据准稳态理论的空气动力分析横向奔腾的确定性动力学，以及由湍流引起的随机波动引起的谱线展宽的随机效应。我们的发现清楚地表明，标准的非线性宏观结构表现出的稳态响应曲线与线性质量－弹簧－阻尼器结构获得的帕金森通用曲线有很大不同。重要的是，由于非线性阻尼，振荡的振幅在上游速度较高时会衰减，而频谱线则由于湍流引起的随机波动和振幅-相位噪声转换而变宽，从而降低了自持振荡的质量。在基于横向疾驰的高效能量收集器的设计中应考虑这两种现象，这是一个快速发展的研究领域。我们的发现清楚地表明，标准的非线性宏观结构表现出的稳态响应曲线与线性质量－弹簧－阻尼器结构获得的帕金森通用曲线有很大不同。重要的是，由于非线性阻尼，振荡的振幅在上游速度较高时会衰减，而频谱线则由于湍流引起的随机波动和振幅-相位噪声转换而变宽，从而降低了自持振荡的质量。在基于横向疾驰的高效能量收集器的设计中应考虑这两种现象，这是一个快速发展的研究领域。我们的发现清楚地表明，标准的非线性宏观结构表现出的稳态响应曲线与线性质量－弹簧－阻尼器结构获得的帕金森通用曲线有很大不同。重要的是，由于非线性阻尼，振荡的振幅在上游速度较高时会衰减，而频谱线则由于湍流引起的随机波动和振幅-相位噪声转换而变宽，从而降低了自持振荡的质量。在基于横向疾驰的高效能量收集器的设计中应考虑这两种现象，这是一个快速发展的研究领域。