气流中变截面柔性矩形薄板的动力特性分析

Dynamic characteristic analysis of flexible rectangular thin plate with variable cross section in airflow

基于理想流体的Euler方程和Euler-Bernoulli梁理论,建立了稳定气流中变截面柔性矩形薄板的颤振模型,考虑变截面柔性板的厚度只沿垂直于几何中面方向呈线性分布,用线性小扰动分析法研究了气流中变截面柔性矩形薄板的动力特性.研究了无量纲波数、薄板的横向位置和不同变截面系数对于变截面柔性矩形薄板的无量纲角频率和无量纲扰动时间增长率的影响,并分析了气流速度对变截面柔性矩形薄板波数和频率的影响,得到了最不稳定颤振时的波数和频率值.

Based on the Euler equation of ideal fluid and Euler-Bernoulli beam theory,the flutter model of flexible rectangular thin plate with variable cross-section in stable airflow is established. Considering that the thickness of flexible rectangular thin plate with variable cross-section is only linearly distributed along the direction perpendicular to the middle of the geometry,the dynamic characteristics of variable cross-section flexible rectangular thin plate in airflow are studied by linear small disturbance analysis method. The effects of dimensionless wave number,transverse position of thin plate and different variable cross-section coefficient on dimensionless angular frequency and dimensionless disturbance time growth rate of flexible rectangular thin plate with variable cross-section are studied.The effects of airflow velocity on wave number and frequency of flexible rectangular thin plate with variable cross-section are analyzed,and the wave number and frequency values under the most unstable flutter are obtained.