超高展弦比无人机的等效几何精确梁动力学建模
EQUIVALENT GEOMETRICALLY EXACT BEAM MODELING FOR ULTRA-HIGH ASPECT RATIO UNMANNED AERIAL VEHICLES
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摘要: 超高展弦比无人机因其优异的气动效率而被广泛采用, 但其轻柔细长结构在飞行中易出现显著的几何非线性变形. 尽管三维有限元方法能够准确模拟此类结构的非线性响应, 但其高昂的计算成本限制了实际应用. 为此, 本文提出了一种面向超高展弦比无人机的等效几何精确梁动力学建模方法, 通过将复杂三维结构转化为由几何精确梁与刚体单元构成的多体系统, 实现高效率的动力学仿真. 以 X-HALE 无人机为研究对象, 针对其主翼、吊杆和尾翼等周期非均匀细长部件, 采用辛传递矩阵法计算等效一维梁的完全耦合截面刚度矩阵, 并基于三维与一维模型动能等效原理及截面速度插值技术, 构建相应的等效梁模型质量矩阵. 在此基础上, 建立由一维几何精确梁与刚体单元刚性连接组成的柔性多体系统, 采用基于对偶四元数的几何精确梁单元. 研究无人机在巡航状态下的静气动弹性配平方法和瞬态动力学数值积分方法. 数值算例表明, 机翼等效梁模型的静力学响应与三维有限元结果吻合良好, 整机等效模型的模态特性与三维模型高度一致, 验证了所建模型的准确性与有效性. 相较于传统三维有限元方法, 本文所提方法在保证计算精度的同时, 显著降低了系统自由度, 为超高展弦比无人机的动力学仿真与设计优化提供了高效的建模手段.Abstract: Ultra-high aspect ratio unmanned aerial vehicles (UAVs) exhibit superior aerodynamic efficiency but are prone to significant geometric nonlinearities due to their lightweight and slender structures. Although three-dimensional finite element models can accurately capture these effects, their high computational cost limits practical application. This study presents an efficient dynamic modeling approach based on equivalent geometrically exact beams for ultra-high aspect ratio UAVs. Complex three-dimensional structures are reduced to a multibody system consisting of geometrically exact beam and rigid-body elements. Using the X-HALE UAV as a case study, fully coupled stiffness and mass matrices of the equivalent beams are derived through the symplectic transfer matrix method and kinetic energy equivalence. A flexible multibody model employing dual-quaternion-based beam elements is then developed to investigate static aeroelastic trim and transient dynamic behavior under cruise conditions. Numerical results demonstrate that the equivalent beam model closely reproduces the static and modal responses of the 3D FE model while significantly reducing computational cost and system degrees of freedom. The proposed method provides an accurate and efficient framework for dynamic simulation and design optimization of ultra-high aspect ratio UAVs.
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