关键词: 扇形薄板, 贝塞耳函数, 波节线, 简单支承, 克拉尼图形

Abstract: Under small flexivity theory，the vertical small vibrations on right-angled sectorial thin plate which placed horizontally with two simply-supported radial edges and cantilevered arc edge is investigated theoretically and experimentally. The normal modes of analytical solutions on thin plate in different eigen frequencies are studied，and the radii of arc-shaped standing waves nodes on the plate are calculated. Furthermore，the laws of equation's eigen - values and the modulus of plate are obtained，and the patterns of standing waves are also observed. Three kinds of standing waves nodes on a metal board are presented: only having radical nodes，only having arc-shaped nodes ( two radial edges excluded) ，and both having radical nodes and arc-shaped nodes. The theoretical values coincide with the experimental results.

Key words: thin sector plate, Bessel functions, standing waves nodes, simply-supported, Chladni patterns