基于能量法的加筋扁球壳轴对称自振缩尺模型研究  

STRUCTURAL SIMILITUDE FOR AXIAYMMETRIC FREE VIBRATION OF STIFFENED SHALLOW SPHERICAL SHELLS BY ENERGY METHOD

作　　者：于伟[1] 李正良[1,2] YU Wei LI Zheng-liang(School of Civil Engineering, Chongqing University, Chnngqing, 400045, China Key Laboratory of New Technology for Construction of Cities in Mountain Area （Chongqing University）, Ministry of Education, Chongqing, 400045, China)

机构地区：[1]重庆大学土木工程学院,重庆400045 [2]山地城镇建设与新技术教育部重点实验室(重庆大学),重庆400045

出　　处：《工程力学》2016年第11期155-162,共8页Engineering Mechanics

基　　金：国家自然科学基金项目(51278511)

摘　　要：该文基于结构体系的总能量进行相似转换,导出了大型加筋扁球壳轴对称振动时模型需满足的广义相似条件和缩尺原理。在此基础上,创新性地引入结构刚度参数公式,重点研究了不完全相似缩尺振动。以正交加强(径-环向加筋)扁球壳为例,基于线性几何方程和壳体最大动能,应用里兹法建立结构的频率方程,分析了模型与原型的完全和不完全相似。结果表明:完全相似缩尺模型能准确地预测原型。不完全相似分析中,当模型与原型的加筋肋满足截面积、一阶矩和二阶矩与对应加筋肋间距比值相似时,模型加筋肋截面可采用与原型不同的形式,为试验模型的设计提供了方便;当模型与原型的材料泊松比相等或相近时,推导的缩尺原理能较好的预测原型结构的动力特性。该文采用的方法和给出的结论对于相关试验和设计具有很好的实用价值。The general similitude conditions and scaling laws are derived by directly applying the similitude transformation to the total energy of a structural system. On this basis, partial similitude of vibration is mainly investigated based on innovative introduction of the formulas for stiffness parameters. A reinforced orthotropic shallow spherical shell is taken as an example for analysis. The frequency equations are obtained based on linear strain-displacement relations and maximum kinetic energy. Completely and partially similar vibrations are performed. The results show that completely similar models can predict the behavior of the prototype accurately. Section types of stiffeners of the model can be different from the ones of the prototype, when the ratios of the cross-sectional area, first and second moment of the stiffener area to their spacing are similar. This is convenient for the design of experiment models. A scaling law of partial similarity is derived when the Poisson＇s ratio of the model is equal or near to the value of the prototype, and the model can predict well the vibration of the prototype. The method and results of this paper have good practical value for relevant experiments and design.

关 键 词：加筋扁球壳 轴对称振动 能量法 最大动能 缩尺原理 

分 类 号：TU392.6[建筑科学—结构工程]