超音速负泊松比蜂窝夹层板颤振分析

Flutter Analysis of Honeycomb Sandwich Plate with Negative Poisson’s Ratio in Supersonic Flow

对超音速流下负泊松比蜂窝夹层壁板颤振问题进行了分析。基于Reddy三阶剪切板理论、小变形理论和一阶活塞理论建立了三维蜂窝夹层壁板的颤振方程。使用Galerkin方法将运动方程进行离散,并使用数值方法进行求解。讨论了蜂窝单元内角、直壁长与斜壁长之比、斜壁壁厚与斜壁长之比和来流马赫数对壁板颤振特性的影响。研究结果表明,随单元内角的增大,临界马赫数和颤振频率先增大后减小。蜂窝单元内角为负时,负泊松比蜂窝板与正泊松比蜂窝板相比,临界马赫数并没有提高,反而在角度较小时,临界马赫数有所下降。可以通过改变单元的直壁长与斜壁长之比、斜壁壁厚与斜壁长之比来提高板的颤振临界马赫数。

Flutter problem of honeycomb sandwich panel with negative Poisson’s ratio in supersonic flow is analyzed.Based on Reddy’s third-order shear theory,small deflection theory and first-order piston theory,the three-dimensional governing equations of honeycomb sandwich panel are established.The discrete ordinary equations of which are obtained by using the Galerkin method,and solved by using numerical simulation method.The effects of the internal angle of the unit,the aspect ratio of the unit sides,the relative thickness and the Mach number on the flutter characteristics of the plate are discussed.The results show that the critical Mach number and flutter frequency increase first and then decrease as the internal angle increases.When the internal angle of the honeycomb unit is negative,the critical Mach number of the negative Poisson’s ratio honeycomb panel is not improved compared with the positive Poisson’s ratio honeycomb panel,but when the angle is small,the critical Mach number decreases.Changing the aspect ratio of the unit sides and the relative thickness has a certain influence on improving the plate’s critical Mach number.