摘要
研究含孔隙金属陶瓷功能梯度圆柱壳在热荷载、弹性基础以及轴向荷载作用下的模态频率。首先,采用Voigt模型以及Sigmoid型分段体积分数模型分析功能梯度材料与温度相关的材料属性;然后,基于Sanders壳体理论和Rayleigh-Ritz法推导出功能梯度圆柱壳的模态频率方程;其次,利用MATLAB编程得到功能梯度壳的模态频率,并通过文献结果及有限元验证模态方程的正确性;最后,研究非线性温升、孔隙率、S型分段体积分数指数、弹性基础等对功能梯度圆柱壳模态频率的影响。结果表明:温度梯度主要对圆柱壳振动波数低于4时的模态频率产生较大影响;增大S型体积分数指数不仅提高结构的模态频率,而且结构受温度的影响也越小;设计功能梯度圆柱壳内部含均匀分布孔隙或外部添加环向基础均可有效提高结构刚度。
The modal frequencies of a metal-ceramic functionally graded porous cylindrical shell subjected to thermal load,elastic foundation and axial load are studied.Firstly,the temperature-dependent material properties of the functionally graded materials are analyzed by using the Voigt model and Sigmoid-shaped piecewise volume fraction model.Then,based on the Sanders shell theory and the Rayleigh-Ritz method,the modal frequency equation of a functionally graded cylindrical shell is derived.Thereafter,the modal frequency of the functionally graded shell is obtained by employing the MATLAB programming,and the correctness of modal equation is verified through the results obtained from literatures and FEA.In the end,the effects of nonlinear temperature rise,porosity,S-shaped volume fraction index,elastic foundation,etc.on the modal frequencies of a functionally graded shell are examined.Results indicate that the temperature gradient mainly has a greater effect on modal frequency as the vibration wave number of the cylindrical shell is lower than 4.Increasing the S-shaped volume fraction index not only increases the modal frequency of the structure,but also weakens the effects of temperature on the structure.Designing a functionally graded cylindrical shell with evenly-distributed porosity inside or adding elastic foundations outside can effectively improve the structural rigidity.
作者
刘超
刘文光
LIU Chao;LIU Wen-guang(School of Aeronautical Manufacturing Engineering,Nanchang Hangkong University,Nanchang 330063,China)
出处
《船舶力学》
EI
CSCD
北大核心
2022年第3期414-425,共12页
Journal of Ship Mechanics
基金
国家自然科学基金资助项目(51965042)
江西省自然科学基金资助项目(20181BAB206023)。
