Department of Mechanical and Industrial Engineering, University of Massachusetts, Amherst, MA 01003, USA.
Soft Matter. 2017 Mar 29;13(13):2465-2474. doi: 10.1039/c7sm00129k.
We study the influence of one or multiple thin spots on the flow-induced instabilities of flexible shells of revolution with non-zero Gaussian curvatures. The shell's equation of motion is described by a thin doubly-curved shell theory and is coupled with perturbed flow pressure, calculated based on an inviscid flow model. We show that for shells with positive Gaussian curvatures conveying fluid, the existence of a thin spot results in a localized flow-induced buckling response of the shell in the neighborhood of the thin spot, and significantly reduces the critical flow velocity for buckling instability. For shells with negative Gaussian curvatures, the buckling response is extended along the shell's characteristic lines and the critical flow velocity is only slightly reduced. We also show that the length scale of the localized deformation generated by a thin spot is proportional to the shell's global thickness when the stiffness of the thin spot is negligible compared with the stiffness of the rest of the shell. When two thin spots exist at a distance, their influences are independent from each other for shells with positive Gaussian curvatures, but large-scale deformations can be created due to multiple thin spots on shells with negative curvatures, depending on the thin spots' relative position.
我们研究了一个或多个薄点对具有非零高斯曲率的旋转柔性壳流致不稳定性的影响。壳的运动方程由薄双曲壳理论描述，并与基于无粘流模型计算的扰动脉压耦合。我们表明，对于正高斯曲率输送流体的壳，薄点的存在会导致薄点附近壳的局部流致屈曲响应，并显著降低屈曲不稳定性的临界流速。对于负高斯曲率的壳，屈曲响应沿壳的特征线扩展，临界流速仅略有降低。我们还表明，当薄点的刚度与壳的其余部分的刚度相比可以忽略不计时，由薄点产生的局部变形的长度尺度与壳的全局厚度成正比。当两个薄点之间存在一定距离时，对于正高斯曲率的壳，它们的影响是相互独立的，但由于负曲率壳上存在多个薄点，可能会产生大规模变形，具体取决于薄点的相对位置。
