换能器布置与四状态简化模型在俯仰-沉浮-襟翼气动翼型颤振后压电能量收集中的局限性

中文摘要 AI 辅助

气动弹性颤振通常是一种需要设计规避的失效模式，然而颤振后的极限环振荡（LCOs）将流动能转化为持续的结构运动，压电换能器可将这种运动转化为电能。换能器嵌入一个具有有限质量后缘襟翼和基于非定常片条理论气动力的三自由度俯仰-沉浮翼型中，构成一个具有三次硬化俯仰弹簧的十五状态电-气动弹性系统。该系统通过将泰勒展开残差双正交投影到耦合雅可比矩阵的特征向量上进行降阶。该测试平台特意采用低阶设计，以便每个降阶预测都能与所替代的全阶系统进行校验。承载换能器的自由度是一个一阶设计变量，因为它同时决定了颤振边界移动的符号和收集功率的大小。降阶模型的误差主要不取决于保留基的规模，而取决于降阶算子如何依赖于低速度。展开保留特征值使降阶算子保持块对角形式，在任何展开阶数下保留模态之间均无耦合；而将精确雅可比矩阵重新投影到相同的冻结基上则提供了这种耦合，并在不扩大基的情况下恢复了结构响应。研究发现，剩余的误差存在于收集电压中，平衡特征向量以与运动固定的比例携带该电压，而将电模态加入基中并不能消除此误差；然而，同一基也遗漏的襟翼检测，则通过保留襟翼模态得以恢复。因此，收集器降阶模型的精度必须针对所收集的量本身进行报告。

英文摘要

Aeroelastic ?utter is normally a failure mode to be designed against, yet the limit-cycle oscillations (LCOs) that follow it convert flow energy into sustained structural motion that a piezoelectric transducer can turn into electrical power. A transducer is embedded in a three-degree-of-freedom pitch-plunge aerofoil with a finite-mass trailing-edge flap and unsteady strip-theory aerodynamics, giving a fifteen-state electro-aeroelastic system with a cubic hardening pitch spring, and the system is reduced by biorthonormal projection of the Taylor-expanded residual onto eigenvectors of the coupled Jacobian. The testbed is deliberately low order, so that every reduced prediction can be checked against the full-order system it replaces. The degree of freedom that carries the transducer is a first-order design variable, since it sets both the sign of the shift in the flutter boundary and the magnitude of the harvested power. The error of the reduced model is dominated not by the size of the retained basis but by how the reduced operator is made to depend on low speed. Expanding the retained eigenvalues leaves the reduced operator block-diagonal, with no coupling between the retained modes at any order of the expansion, whereas re-projecting the exact Jacobian onto the same frozen basis supplies that coupling and restores the structural response without enlarging the basis. It is found that the error that remains lies in the harvested voltage, which the equilibrium eigenvectors carry in a fixed proportion to the motion, and this is not removed by adding the electrical modes to the basis, whereas the flap detection, which the same basis also misses, is recovered by retaining the flap modes. The accuracy of a harvester reduced-order model must therefore be reported on the harvested quantity itself.

发表机构

• Institute of Communications and Computer Systems (ICCS), National Technical University of Athens（雅典国立技术大学通信与计算机系统研究所）
• Department of Environmental Sciences, University of Thessaly（色萨利大学环境科学系）
• DASKALOS APPS（达斯卡洛斯应用公司）

机构由 AI 辅助整理，请以论文原文为准。

补充信息

备注

16 pages; 6 figures;