LAUSR

Numerical methods studied the functionally graded piezoelectric porous (FGPP) microplates are still somewhat restricted. In this study, a size-dependent approach in the framework of isogeometric analysis (IGA) via the modified strain gradient theory (MSGT) and the higher-order shear deformation theory (HSDT) for electro-mechanical vibration analysis of FGPPo microplates is presented for the first time. A FGPP microplate is created from a mixture of two materials which their properties vary continuously through the thickness plate obeying a modified power-law expression. Two porosity distribution types including even and uneven are considered. An electric potential field which satisfies the Maxwell’s equation in the quasi-static approximation is adopted. To study size effects, MSGT is proposed with the addition of three material length scale parameters (MLSPs) into the elastic constants. It is general due to when two or three MLSPs are set equal to zeros, MSGT can be recovered into the modified couple stress theory model (MCST) or classical higher-order shear deformation theory, respectively. Governing equations deduced from the weak form of FGPP microplates are obtained by utilizing the principle of virtual work, subsequently, natural frequencies of FGPP microplates are determined by IGA. The influence of external electric voltages, power-law index, porosity coefficient, porosity distribution, various boundary conditions, and material length scale parameters on the natural frequencies of FGPP microplates is investigated. To demonstrate the reliability and effectiveness of the proposed method, the present results are compared with various available publications in the literature. Moreover, although there are no analytical solutions, we strongly furthermore present answers of some FGPP microplates being considered as reference results for upcoming studies.