A new approach to build geometrically-nonlinear dynamic aeroelastic models is proposed that only uses information typically available in linear aeroelastic analyses, namely a generic (linear) finite-element model and frequency-domain aerodynamic influence coefficient matrices (AICs). Good computational efficiency is achieved through a two-step process: Firstly, a geometric reduction of the structure is carried out through static or dynamic condensation on nodes along the main load paths of the vehicle. Secondly, manipulation of the resulting linear normal modes (LNMs), the condensed stiffness and mass matrices, and the nodal coordinates provides the modal coefficients of the intrinsic beam equations along these load paths. This preserves the LNMs of the original problem and augments them with the geometrically nonlinear terms of beam theory. The structural description is in material coordinates and modal AICs are thus naturally included as follower forces. Numerical examples include cantilever wings built using detailed models, for which effects such as nonlinear aeroelastic equilibrium, nonlinear dynamics and structural-driven limit-cycle oscillations are shown. Results demonstrate the ability of the methodology to seamlessly and efficiently incorporate critical nonlinear effects to (linear) arbitrarily large aeroelastic models of high aspect ratio wings.

提出了一种建立几何非线性动态气动弹性模型的新方法，该方法仅使用线性气动弹性分析中通常可用的信息，即通用（线性）有限元模型和频域气动影响系数矩阵（AIC）。通过两步过程可以实现良好的计算效率：首先，通过在沿车辆主载荷路径的节点上进行静态或动态压缩来对结构进行几何简化。其次，对所得线性法线模（LNM），压缩刚度和质量矩阵以及节点坐标的操纵提供了沿这些载荷路径的固有梁方程的模态系数。这样可以保留原始问题的LNM，并用射束理论的几何非线性来扩充它们。结构描述以材料坐标表示，因此模态AIC自然也包含在跟随力中。数值示例包括使用详细模型构建的悬臂机翼，并显示了非线性气动弹性平衡，非线性动力学和结构驱动的极限循环振荡等影响。结果证明了该方法能够无缝地和有效地将关键的非线性效应纳入高纵横比机翼的（线性）任意大型气动弹性模型中。