摘要
本文对基于Mindlin理论所导出的厚截锥壳的一阶基本微分方程组采用了子结构离散变量法,求解了这类结构的固有频率和相应的振型。文中给出了算例,其结果与试验结果和有限无法计算结果相比是令人满意的。
A truncated conical shell is an important structural component in all industrial applications.Analysisof the vibration of the shell is of great importance.When the shell is too thick,the Kirchihherf theory ofthin shells is no longer available.In this paper,from the theory of plates and shells and the Mindlin as-sumption,a set of first-order differential equations with respect to the ten state parameters of a thick trun-cated conical shell are derived.The differential equations are then solved by using the discrete-variablemethod,in which the relationship of the state parameters between the two boundary points is obtained bysolving the initial value problem,and the frequency equation is established.In order to increase the accura-cy and the steadiness of the solution,a sub-structure method is proposed in which a thick truncated conicalshell is divided into a number of sub-structures and the Riccati transform is used to transfer the state pa-rameters through all sub-structures.In the end of the paper two examples,a free disk with two different thicknesses,and a bevel gear,arepresented and the results are compared with those of experiment,those of finite element method and thosereported by other investigators utilizing different analytical and numerical techniques.The examples showthat the accuracy of the present method is satisfactory and has a high steadiness.
出处
《振动工程学报》
EI
CSCD
1993年第3期287-291,共5页
Journal of Vibration Engineering
基金
航空青年基金
关键词
厚壁
壳体
自由振动
离散变量法
子结构法
thick wall shell
free vibration
discrete variable method
substructure method
Riecati transform
