颤振系统中一个特殊的几何缩比效应  

A special geometrical scaling effect in flutter systems

作　　者：杨智春[1] 张飞霆 赵令诚[1] 

机构地区：[1]西北工业大学航空学院结构动力学与控制研究所,西安710072

出　　处：《中国科学：物理学、力学、天文学》2014年第3期293-298,共6页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：国家自然科学基金(批准号:11072198;11102162);高等学校学科创新引智计划(编号:B07050)资助项目

摘　　要：颤振是弹性结构在气流中发生的一种动力学不稳定现象,确定颤振系统的颤振临界速度和颤振频率是颤振分析的主要目的.数值分析和模型试验是确定系统颤振特性的两个主要手段.本文根据相似理论的第二定理,通过量纲分析证明,对于任何线性颤振系统,在结构材料保持不变的情况下,几何尺寸放大或者缩小n倍,颤振系统的固有振动频率和颤振频率相应的缩小或者放大n倍,而颤振临界速度保持不变.通过简支均匀梁和四边简支板的固有频率公式以及曲壁板颤振临界速度和颤振频率的数值算例,验证了该结论.颤振系统这种特殊的几何缩比效应揭示了在模型风洞颤振实验中,由于要对颤振临界速度进行缩比设计,因此必须使用与原型结构不同属性的材料.Flutter is a dynamic unstable phenomenon of elastic structure in airflow, the main objective of flutter analysis is to obtain the flutter critical speed and flutter frequency of flutter system. Numerical simulation and model test are two preliminary measures of determining the flutter characteristics of the system. According to the second theorem of similarity theory, it is proven by dimensional analysis that for any linear flutter system, if the geometrical size of the model is enlarged or reduced by n times while the material properties keep the same, the natural frequencies and flutter frequencies will be reduced or enlarged by n times accordingly, but the flutter critical speed remains unchanged. This finding is verified by formulations of the natural frequency for a simply supported uniform beam and a rectangular plate with simply supported edges, together with the numerical simulation example of the flutter critical speed and frequency of a curved panel. The special geometrical scaling effect in flutter reveals that in the model flutter wind tunnel tests, materials different from those of the prototype structure must be used considering that the flutter critical speed will be usually scaled.

关 键 词：颤振临界速度 固有频率 几何缩比 量纲分析 动力学相似 

分 类 号：V215.34[航空宇航科学与技术—航空宇航推进理论与工程]