Due to corner stress singularities, free vibration analysis of thin sectorial plates with arbitrary boundary supports including a free vertex is a rather challenging problem. In this paper, a novel rotation-free quadrature element formulation based on Kirchhoff plate theory is presented to solve the problem. Different from all existing quadrature thin plate element formulations, rotational degrees of freedom are not used. Instead, a boundary point is modeled by two nodes separated by a very small distance and thus the $C^1$ continuity is easily enforced. Explicit formulations with arbitrary number of nodes and nodes of any type are worked out to ease the p-refinement. Numerical results demonstrate that the proposed formulation is simple, straightforward and has excellent performance for solving thin sectorial plate with arbitrary combinations of boundary supports. Some tabulated data are believed new which may serve as a reference.

由于角应力奇异，具有任意边界支撑（包括自由顶点）的薄扇形板的自由振动分析是一个相当具有挑战性的问题。在本文中，提出了一种基于基尔霍夫板理论的新型无旋转正交单元公式来解决该问题。与所有现有的正交薄板单元公式不同，不使用旋转自由度。取而代之的是，一个边界点由两个相距很小的节点建模，因此${丙}^1$连续性很容易实现。计算出具有任意数量节点和任何类型节点的显式公式以简化p细化。数值结果表明，所提出的公式简单、直接，并且在求解具有任意边界支撑组合的薄扇形板方面具有出色的性能。一些列表数据被认为是新的，可以作为参考。