四角点支承四边自由矩形板自振分析新方法

许琪楼

振动与冲击 ›› 2013, Vol. 32 ›› Issue (3) : 83-86.

PDF(730 KB)
PDF(730 KB)
振动与冲击 ›› 2013, Vol. 32 ›› Issue (3) : 83-86.
论文

四角点支承四边自由矩形板自振分析新方法

  • 许琪楼
作者信息 +

A NEW ANALYSIS ON FREE VIBRATION OF A RECTANGULAR PLATE WITH FOUR FREE EDGES AND FURE CORNER POINT SUPPORTS

  • XU Qi-lou
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文章历史 +

摘要

四角点支承四边自由矩形板振形函数表达式由四边自由板所固有的基本振形和角点力所激发的附加振形组成。振形函数要满足振动微分方程和板挠度与角点力间的微分关系。为表示矩形板双向振动规律,基本振形在二个坐标轴方向分别有各自的表达式,并符合对应方向边界所限定的变形和受力特征:在对应自由边界上振幅不为零而剪力分布为零值,在自由角点处对应的四个角点力均为零值。而附加振形在角点处的振幅与角点力要符合板弯曲理论中的微分关系,在四个自由边界上对应的剪力分布均为零值。这种方法克服了现有解法中的理论缺陷,计算理念更合理。

Abstract

The vibration mode expression of the rectangular plate with four free edges and four corner point supports is composed of the two parts: the first is the basic intrinsic mode of the plate with four free edges, the second is the addition mode aroused by the four corner forces. The vibration mode function must satisfy the vibration differential equation and the differential relation between the corner force and the bending deflection. For to indicate the bi-directional vibration, the basic mode has the alone expression along the two coordinate axis respectively, which accord with the load-deformation characteristic limited by the relevant edges.The character is the zero shear force and the non-zero amplitude at the relevant free edges and the zero corner forces at the four corners. The addition mode must satisfy the differential relation between the corner force and the bending deflection at the four corner points, and its shear force is zero and the amplitude is not zero at the four free edges. The new method surmounts the theory drawback in original method, and the compute idea is reasonable.

关键词

弹性振动 / 矩形板 / 角点支承 / 基本振形 / 附加振形

Key words

elastic vibration / rectangular plate / corner point support / basic mode / addition mode

引用本文

导出引用
许琪楼. 四角点支承四边自由矩形板自振分析新方法[J]. 振动与冲击, 2013, 32(3): 83-86
XU Qi-lou. A NEW ANALYSIS ON FREE VIBRATION OF A RECTANGULAR PLATE WITH FOUR FREE EDGES AND FURE CORNER POINT SUPPORTS[J]. Journal of Vibration and Shock, 2013, 32(3): 83-86

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