基于微分求积法的轴向流作用下叠层板的稳定性和模态分析

Buckling and modal analysis of coupled parallel flexible plates in an axial flow using the differential quadrature method

分析了轴向流作用下两端简支和固支叠层板的稳定性和模态特性。基于势流理论建立轴向流作用下叠层板的流固耦合系统连续型运动方程,采用微分求积法对连续型运动方程进行离散,流场势函数用板的横向振动位移变量来表示,得到关于叠层板的横向振动位移变量的控制方程。求解控制方程的广义特征值,计算分析结果表明,两端简支和两端固支模型发生屈曲失稳,且得到了屈曲失稳临界速度与叠层板的层数和板间距的关系;轴向流作用下叠层板的一阶模态并不是叠层板的同相弯曲模态。

The stability and dynamics of the parallel plates with simply supported （or clamped）boundary conditions in uniform axial flow were studied.Flow viscosity and elastic damping are neglected,and the flow around the plates is assumed potential. The governing equations of coupled parallel flexible plates in axial flow were derived.The differential quadrature method was employed to discrete the governing equation and the flow potential function.The governing equation can be expressed as the function of structural transverse vibration displacement by the matrix operations.The eigenvalue method was used to analyze the results of the coupled parallel flexible plates,the results of which show that the models with simply supported （or clamped）boundary conditions undergo buckling instability when flow velocity reaches the critical value.The effects of their rel-ative distance and the number of plates on critical flow velocities were discussed.The first mode of the coupled parallel flexible plates is not the in-phase mode.