关键词: 非规则边界薄板, 变分微分求积法, Voronoi图, 无网格法, 热振动

Abstract: A meshless variational differential quadrature (VDQ) method is proposed for plates with irregular geometric configurations. By integrating differential reproducing kernel 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 plates with five typical boundary shape, 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 maxi-mum deflection magnitudes for both type plates exhibit a order: 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.

Key words: irregular boundary thin plates, variational differential quadrature method (VDQ), Voronoi diagram, meshless method, thermal vibration