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In the present work, the vibration response of the porous functionally graded piezoelectric plates with electro-thermal loading using finite element formulations has been studied. A sigmoid law is used for the material property deviation along the thickness direction. The first-order shear deformation theory (FSDT) with von Karman nonlinear strains and Hamilton's principle is used to obtain the governing equations. The governing equations are solved by finite element methods with 9-noded iso-parametric rectangular elements with 7 degrees of freedom (DOFs) per node. The accuracy of the results is evaluated by comparing them with the results available in the literature. The analysis shows that the  uneven type  porosity distribution gives a larger nondimensional frequency than the  even type  porosity distribution FGP plate. The non-dimensional frequency decreases with increases in theratio. Among all the conditions, CCCC boundary conditions have a larger frequency than SSSS, SFSF, SFCF, and CFFF. The obtained frequency under applied electric loading depends on the magnitude and the applied voltage sign. As the temperature changeincreases with the porosity exponentof the FGP plate, the nondimensional frequency is also increasing. The obtained results can design a porous FGP material-based smart composite structure under a thermo-electric environment.

Vibration response analysis of sigmoidal functionally graded piezoelectric (FGP) porous plate under thermo-electric environment