含分层损伤复合材料层合板非线性动力稳定性

Nonlinear dynamic instability behavior of delaminated composite laminates

采用Reddy的板高阶剪切变形简化理论研究了含分层损伤复合材料层合板的非线性动力稳定性问题。建立了分层模型,推导了考虑几何非线性和阻尼效应的Methieu方程,给出了该方程的解析解表达式;研究了参数振动解的稳定性;然后通过典型数例讨论了分层损伤对层合板固有频率、屈曲临界力以及动力稳定区域的影响;研究了保守与非保守体系的外载荷的激励频率对层合板第一参数振动的振幅的影响,以及线性、非线性阻尼对非保守体系的最大牵引深度的影响。由典型算例讨论可知,随着复合材料层合板分层损伤的扩大,其动力稳定性能逐渐减弱,特别是损伤接近层合板的中面时,分层损伤对其动力稳定性能的影响最大。

Nonlinear instability associated with composite laminates with a delamination under dynamic loads was studied. A dynamic instability equation, called Methieu equation, considering the nonlinear elastic and damping effects, was deduced and the corresponding solution in terms of analytical expressions was obtained on the basis of Reddy＇s simple higher order shear deformation theory and the delaminnation model developed by the authors. The dynamic instability of the parameter vibration was investigated. From some typical examples, it is clear that the effects of delamination lengths and locations on the natural frequency, buckling load and instability regions, and the effect of excitation frequency of dynamic load on the amplitude of the first parameter vibration are significant. The influence of linear and nonlinear damping on the maximum deepness of ＂traction＂ is discussed. Some typical examples indicate that the dynamic instability behavior of the laminates gradually decreases with increasing delamination; especially, when delamination is close to the mid-plane of the laminates, the influence of delamination on the dynam- ic instability behavior of the laminates is most remarkably.