变角度纤维复合材料层合斜板的颤振分析  

Flutter Analysis of Laminated Skew Plates with Variable Angle Tows

作　　者：胡寒[1] 聂国隽[1] HU Han;NIE Guojun(School of Aerospace Engineering and Applied Mechanics,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《力学季刊》2020年第1期69-79,共11页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11772232,11372225)。

摘　　要：假设纤维方向角沿层合板的长度方向线性变化,研究了变角度纤维复合材料层合斜板的颤振.通过坐标变换将斜板变换为正方形板,采用层合板表面连续变化的速度环量来模拟空气对其的作用,速度环量分布利用Cauchy积分公式计算.建立了系统的Lagrange方程并采用Ritz法得到了层合板的自振频率和颤振/不稳定性分离临界速度.通过数值算例验证了本文模型和方法的正确性和收敛性,分析了各个铺层内纤维方向角的变化对自振频率和颤振/不稳定性分离临界速度的影响.研究结果表明,通过纤维的变角度铺设,可有效地提高层合板的基频和颤振/不稳定性分离临界速度.经合理设计的变角度复合材料层合板具有抑制颤振的作用.Assuming that the fiber orientation varies linearly along the length of the laminated plate, the flutter analysis of laminated skew plates with variable angle tows(VAT) was carried out in this paper. The skew plate was transformed into the square plate by coordinate transformation. The action of the airflow on the laminated plate was simulated by the velocity circulation of the surface of the plate. The Cauchy integral formula was used to calculate the velocity circulation. The Lagrange equation of the system was established and the natural frequency and the flutter/divergence critical speed of VAT laminate were obtained by Ritz method. The accuracy and convergence of the method were verified by numerical examples and the influence of the variation of the fiber orientation angle was analyzed. The results show that the natural frequency and the flutter/divergence critical speed of VAT laminated skew plates can be effectively improved by rational design and thus the effect of the flutter is suppressed.

关 键 词：变角度纤维复合材料 任意四边形层合板 颤振 CAUCHY积分公式 LAGRANGE方程 

分 类 号：O343[理学—固体力学] O347[理学—力学]