褶皱发展对平面张拉薄膜屈曲后动力特性的影响

THE INFLUENCE OF WRINKLES ON VIBRATION OF BUCKLED TENSION PLANE MEMBRANE

剪切位移荷载作用下,平面张拉薄膜经历缺陷、临界褶皱和宏观褶皱3种状态。该文依次分别对处于3种状态的薄膜进行自振特性分析,并明确了3种状态的划分原则。计入平面张拉薄膜的微小抗弯刚度,采用ANSYS/LS-DYNA中显式-隐式连续求解的方法对屈曲后薄膜的动力特性进行分析。依据忽略面外变形的理想模型自振特性分析结果,把平面张拉薄膜的振型划分为贯通振型和间断振型,贯通振型又划分为纵向贯通振型和横向贯通振型。研究结果表明:薄膜处于缺陷状态时,面外变形对薄膜自振特性的影响可以完全忽略,受主应力分布的影响,低阶振型中纵向贯通振型更易于出现,纵向贯通振型的波峰或波谷数量随着频率阶数的递增而规律递增。临界褶皱状态,薄膜的各阶频率均随剪切位移的增加而出现大幅波动,面外变形对薄膜振型的影响逐渐增大,横向贯通振型消失,纵向贯通振型的递增规律逐渐破坏;宏观褶皱状态,薄膜的各阶频率趋于稳定,其主应力分布及振型受面外变形的影响显著。

Under a shearing displacement, the membrane experienced three states, defined as an imperfection state, a critical wrinkles state and a macro wrinkles state. The influences of wrinkles in different stages on the free vibration of a membrane were studied and the division principle of the three states was given more clearly. Considering the small bending rigidity of the tension plane membrane, the explicit-to-implicit sequential solution of ANSYS/LS-DYNA was adopted to analyze the dynamic characteristics of the post-buckling tension membrane. According to the analytical results of the ideal membrane, in which the out-plane deformation was ignored, its vibration modes could be divided into two types, through-vibration modes and local vibration modes. Through-vibration modes can be further divided into vertical-through vibration modes and horizontal-through vibration modes. The results show that, in the imperfection state, the effects of wrinkles on free vibration characteristics could be completely negligible. Affected by the distribution of the principal stress, the vertical-through vibration modes appear more easily in low order modes. Its peaks and troughs increase regularly with the increase of order. In the critical-wrinkle state, each frequency fluctuates wildly. The influence of wrinkles begins to be prominent, horizontal-through vibration modes disappear gradually, and the increasing law of vertical through vibration modes is destroyed. In the macro-wrinkle state, each frequency becomes stable. The out-of-plane deformation has great influences on the principal stress and modes.