针对具有非规则几何形状的薄板结构，提出了一种无网格变分微分求积方法（VDQ），通过融合微分再生核（DRK）插值与径向基函数近似，构建了适用于非结构化节点的微分算子；同时基于Voronoi图理论获得了自适应积分算子，实现了非规则计算域的精确数值积分。通过对方形板、圆角缺损板、方角缺损板、含圆洞板及含方洞板等典型边界形状的单层板与功能梯度板（FGM）开展热致振动特性研究，验证了该方法的有效性。数值结果表明：与传统网格方法相比，无网格VDQ方法减少了节点数量且仍能保持工程精度要求；热致振动分析中，2类薄板的最大挠度均呈现显著递减趋势：方形板>圆角缺损板>方角缺损板>圆洞板>方洞板，揭示了非规则几何形状边界对薄板结构热振动响应的影响规律。本研究为航空航天、精密机械等领域的复杂薄板结构热振动分析提供了高效可靠的数值工具。

A meshless Variational Differential Quadrature （VDQ） method is proposed for thin plates with irregular geometric configurations. By integrating Differential Reproducing Kernel （DRK） interpolation technique and radial basis function approximation， a differential operator suitable for unstructured nodes is constructed. Meanwhile， an adaptive integral operator based on Voronoi diagram theory is developed to achieve numerical integration over irregular computational domains. The effectiveness of this method is validated through systematic investigations of thermally driven vibrations in both homogeneous single-layer plates and Functionally Graded Materials （FGM） with five typical boundary shapes， including square plates， round-corner-defective plates， square-corner-defective plates， circular-hole plates， and square-hole plates. Numerical results demonstrate that compared with traditional grid-based methods， the meshless VDQ method reduces the number of nodes while maintaining engineering accuracy requirements. In thermal-vibration analysis， the maximum deflection magnitudes for both types of plates exhibit a significant decrease trend： intact > round-corner-defective > square-corner-defective > circular-hole > square-hole， revealing the influence mechanism of irregular geometric boundaries on thermal-vibration responses of thin plate structures. This research provides an efficient and reliable numerical tool for thermal-vibration analysis of complex thin plate structures in aerospace， precision machinery， and other engineering fields.