轴向可伸缩悬臂复合材料层合板的建模及数值分析

Modeling and Numerical Analysis of Telescopic Cantilever Composite Plate

论文研究了受面内激励和三阶气动力联合作用下的可伸缩悬臂复合材料层合板的非线性振动问题.根据经典层合板理论和Hamilton原理建立可伸缩悬臂复合材料层合板在匀速轴向外伸和回收过程中的非线性动力学偏微分方程,然后采用Galerkin方法将偏微分方程离散成带有时变系数的常微分方程,通过数值方法得到频率变化图、时间历程图和相图,讨论轴向移动速度、宽厚比对可伸缩悬臂复合材料层合板的动力学特性的影响.结果表明,可伸缩悬臂板匀速外伸时,轴向速度越大可能越易出现振幅发散,回收过程未发现振幅发散现象.

The nonlinear vibration of the telescopic cantilever composite plate subjected to the in-plane excitation and the third-order aerodynamic force is studied when it is in the deployment and retraction.Based on classical laminated plate theory and Hamilton principle,the nonlinear partial differential equation of the telescopic cantilever plate in the process of deployment and retraction is established.Then,the Galerkin method is used to discrete the nonlinear partial differential equation into the ordinary differential equation with time-varying coefficients.Frequency variation diagrams,time history diagrams and phase diagrams are obtained by numerical methods.The influence of axial velocity,width-to-thickness ratio on the nonlinear dynamic characteristics of the telescopic cantilever composite plate is discussed.The results show that the larger the axial moving speed is,the more likely it is to cause the amplitude to diverge when the telescopic cantilever plate is deploying at a uniform speed.However,amplitude divergence does not occur in the retracting process.