A Two Variable Refined Plate Theory for Isogeometric Vibration Analysis of The Functionally Graded Piezoelectric Microplates with Porosities

Abstract

In this article, a free vibration analysis of the functionally graded porous piezoelectric (FGPP) microplates is firstly solved by using a combination of two variable refined plate theory (RPT), modified strain gradient theory (MSGT) and isogeometric analysis (IGA). The FGPP microplate is composed of piezoelectric material with pores, which are distributed across the plate thickness in uniform and non-uniform distributions. The modified strain gradient theory is used to capture the size effect on the natural frequency of the FGPP microplates. According to the variational principle of RPT with two variables, the governing equations are derived and solved by the IGA. The influence of the length scale parameters (LSPs), external electric voltage, power law index, length-to-thickness ratio, aspect ratio and boundary conditions (BCs) on the natural frequency of the FGPP microplates is studied. The numerical results show that a rise in the porosity coefficient makes a decrease in the microplate’s stiffness, while an increase in LSPs leads to a rise in the microplate’s stiffness.

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