弹性支撑功能梯度压电多孔微圆柱壳的自由振动分析

Free vibration analysis of a functionally graded piezoelectric porous cylindrical microshell resting on elastic foundation

旨在研究热-力-电载荷下弹性支撑功能梯度压电多孔微圆柱壳的自由振动。首先,建立弹性支撑功能梯度压电多孔微圆柱壳动力学模型;然后,应用三阶剪切变形壳体理论和修正的偶应力理论,推出弹性支撑功能梯度压电多孔微圆柱壳模态频率的解析解;最后,通过数值算例分析了微圆柱壳模态频率的影响因素。结果表明:Pasternak弹性支撑比Winkler弹性支撑更有利于提高微圆柱壳的模态频率;改变弹性支撑的刚度系数、轴向力、外加电压、孔隙分布、材料体积分数指数和结构尺寸可调节微圆柱壳的模态频率;孔隙体积分数越大,温度或轴向力对模态频率的影响越大,而电压对模态频率的影响则越小;不同材料指数下,增大孔隙体积分数对模态频率的影响趋势不同;弹性支撑会减弱温度、轴向力和电压对模态频率的影响,对薄圆柱壳或短圆柱壳模态频率的影响较为显著。

This article studies the free vibration of a functionally graded piezoelectric porous cylindrical microshell resting on elastic foundation under thermo-electro-mechanical loads.First,the dynamic model of the functionally graded piezoelectric porous cylindrical microshell resting on elastic foundation was established.Then the analytical solution of modal frequencies of the functionally graded piezoelectric porous cylindrical microshell resting on elastic foundation was derived using the third-order shear deformation shell theory and the modified couple stress theory.Last the factors affecting model frequency were discussed by numerical case studies.The results show that the Pasternak foundation is preferred to improve the modal frequencies of the shell to the Winkler foundation.The modal frequencies of the cylindrical microshell could be adjusted via changing the stiffness coefficients of the elastic foundation,axial load,applied voltage,porosity distribution,material volume fraction indexes,and structure dimensions.The larger the porosity volume fraction,the greater the influence of temperature and axial load on the modal frequency,and the smaller the influence of applied voltage on the modal frequency.The change trends of modal frequency with increasing porosity volume fraction are obviously different with different material volume fraction indexes.The elastic foundation can weaken the influence of temperature,axial load and applied voltage on the modal frequency,and its influence on the modal frequency of thin or short cylindrical shell is more significant.