In this study, the vibration stability (i.e., static divergence) and critical velocity of fluid-conveying, ring-stiffened, truncated conical shells are investigated under various boundary conditions. The shell is characterized using Sanders’ theory, while the fluid is modeled using a velocity potential approach with the impermeability condition at the fluid-shell interface. Using linear superposition, the natural frequencies corresponding to each flow velocity are determined by satisfying the dynamic characteristic equation and boundary conditions. Critical velocities are identified where the natural frequencies vanish, indicating static divergence. Parametric studies are conducted to investigate the effect of ring stiffeners on the critical velocities with respect to the semi-cone angle, number of rings, and boundary conditions. The proposed model is validated through comparison with published data. It is found that the rings significantly affect the stability of the cone under different boundary conditions. Instability in stiffened shells occurs at higher critical fluid velocities than in unstiffened shells across all boundary conditions. An increase in the vertex angle leads to a decrease in critical flow discharge.

中文翻译：

---

研究流动流体作用下环加强锥壳动态不稳定性的有限元模型


在这项研究中，研究了各种边界条件下流体输送、环加强、截锥形壳的振动稳定性（即静态发散）和临界速度。使用桑德斯理论来表征壳体，而使用速度势方法以及流体-壳体界面处的不渗透条件对流体进行建模。利用线性叠加的方法，通过满足动力特征方程和边界条件，确定各流速对应的固有频率。临界速度是在自然频率消失的地方确定的，表明静态发散。进行参数研究是为了研究环形加强筋对半锥角、环数和边界条件的临界速度的影响。通过与已发布的数据进行比较来验证所提出的模型。研究发现，环在不同边界条件下显着影响锥体的稳定性。在所有边界条件下，加劲壳中的不稳定性发生在比非加劲壳更高的临界流体速度下。顶角的增加导致临界流量的减少。