In this paper, the nonlinear characteristics of motion-induced aerodynamic forces on large-scale hyperbolic paraboloid roofs are numerically investigated using LES (large-eddy simulation). The mean and standard deviation (STD) of wind pressure coefficients on the rigid hyperbolic paraboloid roofs in the turbulent boundary layer are first simulated to validate the numerical models. Then the hyperbolic paraboloid roofs under forced excitation with different oscillation amplitudes are simulated to study the wind pressures on and the flow structures above the roofs. Moreover, the motion-induced aerodynamic forces, which are represented by the aerodynamic stiffness and damping forces, are also investigated with the harmonic balance method (HBM). It is found that the aerodynamic stiffness force is linearly proportional to the oscillation amplitude, but the aerodynamic damping force is nonlinearly dependent on the oscillation amplitude. The wind-induced responses of the large-scaled roof considering nonlinear motion-induced aerodynamic forces exhibit typically hardening non-Gaussian characteristics at the low reduced frequency, which are consistent with the probabilistic features of vortex-induced vibration (VIV) of slender structures.

在本文中，使用LES（大涡模拟）数值研究了大型双曲抛物面屋顶上运动引起的空气动力的非线性特性。首先模拟湍流边界层中刚性双曲抛物面屋顶风压系数的平均值和标准差（STD）以验证数值模型。然后模拟了不同振幅强制激励下的双曲抛物面屋顶，研究了屋顶上的风压和流动结构。此外，还使用调和平衡法 (HBM) 研究了由空气动力刚度和阻尼力表示的运动引起的空气动力。发现气动刚度力与振荡幅度成线性比例，但气动阻尼力非线性地依赖于振荡幅度。考虑非线性运动引起的气动力的大型屋顶的风致响应在低降低频率下表现出典型的硬化非高斯特性，这与细长结构的涡激振动（VIV）的概率特征一致。