弹性支撑功能梯度微圆柱壳模态频率的研究

Study on modal frequency of a functionally graded cylindrical microshell with an elastic support

在建立弹性支撑功能梯度薄壁微圆柱壳模型的基础上,基于修正的偶应力理论和一阶剪切变形理论,推导了微圆柱壳的模态频率方程,讨论了弹性支撑、尺寸效应、温度梯度、材料组分指数、孔隙以及几何尺寸等参数对微圆柱壳模态频率的影响。结果表明:微尺度下,弹性刚度系数在0~105N/m^(3)范围内对微圆柱壳的模态频率基本无影响,剪切刚度系数在0~5×10^(4)N/m范围内对模态频率的影响较大,且增大剪切刚度系数有益于提高微圆柱壳的模态频率;由修正的偶应力理论得到的模态频率大于由经典连续体理论得到的模态频率;在弹性支撑和尺寸效应有无考虑的4种组合下,模态频率随温度梯度和微圆柱壳长度的增大而减小,随陶瓷体积分数指数的增大而增大,随孔隙体积分数和微圆柱壳厚度的变化规律不同;温度梯度对考虑尺寸效应或弹性基础的微圆柱壳模态频率影响较大,而孔隙调节具弹性支撑微圆柱壳的模态频率尤其显著。

Based on a functionally graded thin-walled cylindrical microshell model with elastic support,the modal frequency equation was derived by using the modified couple stress theory and the first-order shear deformation theory.The impacts of the elastic support,size effect,temperature gradient,material component index,pore and geometry dimensions on the modal frequencies of the cylindrical microshell were studied.Results indicate that the impacts of elastic stiffness coefficient on the modal frequencies can be neglected in the range of 0 to 105 N/m^(3),but the shear stiffness coefficient has a great influence on the modal frequencies in the range of 0 to 5×10^(4) N/m.Moreover,increasing the shear stiffness coefficient is beneficial to increasing the modal frequencies.The modal frequencies obtained by modified couple stress theory are larger than those obtained by classical continuum theory.With or without elastic support and size effect,the modal frequencies decrease with the increase of the temperature gradient and the length of the cylindrical microshell,and increase with the increase of the ceramic volume fraction index.The change laws of the modal frequencies are different with the variation of the pore volume fraction and thickness of the cylindrical microshell.The temperature gradient has a great influence on the modal frequencies of the cylindrical microshell considering size effect or elastic foundation.The influence of pore on the modal frequencies with elastic foundation is especially obvious.