Three Dimensional Elasticity Solution for Vibration Problem of Thick Plate
-
摘要: 本文以弹性动力学的基本方程为基础,推导出厚板的控制方程.给出了在横向强迫力作用下,厚板的应力、位移的动力响应.得出厚板的振动特征是由对称振动、反对称振动和剪切振动的三种模式组成.最后,将简支厚方板作为实例导出自振频率的特征方程,数值计算结果与经典理论、中厚板理论的结果作了比较.Abstract: In this paper,based upon the basic equations of three dimensional theory of elastodynamics,the governing differential equations of thick pla ie have been formulated.The dynamic response of stress and displacement of thick plate subjected to the transversed forced are obtained.It is shown that the vibrational characters of thick plate consist of three modes:thickness shear mode,symmetric mode and anti-symmetric mode.The characteristic equations of simply supported thick plate are derived and the comparison of the free vibration frequencics based on the classic theory,middle thickness plate theory and three dimensional elasticity theory are given.
-
Key words:
- thick plate /
- free vibration /
- forced vibration
-
[1] 曹国雄,《弹性矩形薄板振动》,中国建筑工业出版社,北京(1983). [2] 曹志远,《厚板动力学理论及其应用》,科学出版社,北京(1983). [3] 钱伟长,不用 Kirchhoff 假设的弹性板理论初探,上海工业大学学报,15(1)(1994),1-26. [4] 曾德顺,厚圆柱壳的非轴对称自由振动,同济大学学报,22(3)(1994),274-278. [5] Stephen Barnett,Matrix Methods of Engineers and Scientists,McGraw-Hill Book Co.(UK)(1979). [6] 王飞跃、何福保,用弹性力学方法研究横观各向同性四边简支矩形平板的自由振动问题,固体力学学 报,6(4)(1985),429-435. [7] R.D.Mindlin,Influence of rotatory inertia and shear on fiexcural motions of isotropicelastic plates,J.Appl.Mech.,18,1(1951),31-38. -
计量
- 文章访问数: 2379
- HTML全文浏览量: 159
- PDF下载量: 939
- 被引次数: 0
下载:
渝公网安备50010802005915号