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.
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