东北大学学报（自然科学版）

东北大学学报(自然科学版) ›› 2009, Vol. 30 ›› Issue (9): 1365-1368.DOI: -

• 论著 • 上一篇    

用功的互等定理求解三角形板的固有频率

于政文;吕鹏宇;   

  1. 东北大学理学院;
  • 收稿日期:2013-06-22 修回日期:2013-06-22 出版日期:2009-09-15 发布日期:2013-06-22
  • 通讯作者: Yu, Z.-W.
  • 作者简介:-
  • 基金资助:
    国家高技术研究发展计划项目(2006AA04Z408)

Reciprocal theorem of work done for the solution of natural frequency of triangular plate

Yu, Zheng-Wen (1); Lü, Peng-Yu (1)   

  1. (1) School of Sciences, Northeastern University, Shenyang 110004, China
  • Received:2013-06-22 Revised:2013-06-22 Online:2009-09-15 Published:2013-06-22
  • Contact: Yu, Z.-W.
  • About author:-
  • Supported by:
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摘要： 针对具有复杂边界条件的板的弯曲和振动问题,利用薄板自由振动微分方程与薄板弹性曲面微分方程在形式上和力学上的相似性,基于虚功原理,将薄板振动问题的惯性力视为薄板弯曲问题的横向载荷,将功的互等定理用于求解动力学问题,得到薄板固有频率公式.通过设定合适的振型函数,用功的互等定理、映像法和叠加法,求出简支等腰直角三角形板和等边三角形板的固有频率.采用静力学方法和功的互等定理求解动力学问题很容易得到推广.该方法非常简单,精度较高,是求解结构固有频率的一种好方法.

关键词: 薄板, 功的互等定理, 固有频率, 振型函数, 动力学

Abstract: Based on the principle of virtual work and the differential equation similarity of the free vibration to the elastic curved surface of sheet in both expression and mechanics, the inertia force due to sheet vibration is regarded as the transverse load to bend the sheet, and the reciprocal theorem of work done is used to solve the dynamic problem, thus obtaining the formula of natural frequency of sheet. Setting an appropriate vibration mode shape function, the natural frequency of simply-supported sheet in shape of isosceles right triangle or equilateral triangle is solved via the reciprocal theorem of work done, mapping and superposition. The method combining statics with the reciprocal theorem of work done to solve dynamic problems is easy to extend, and it is simple with high accuracy in solving the natural frequancy of a structure.

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