Computational modeling of sigmoid functionally graded material (SFGM) plate

The first-order shear deformation theory (FSDT) was used to explore the natural frequency response of functionally graded piezoelectric plates subjected to static electrical and mechanical strain in this present study. A monomorph model for a functionally graded piezoelectric plate with material properties that change according to sigmoid law with respect to plate thickness has been considered. A three-dimensional finite element model with a free tetrahedral element mesh was created using COMSOL 4.2 Multiphysics(& REG;) software, with each node having three degrees of freedom. Variations in the FGPM plate's free vibration boundary conditions, composition, and geometry have all been investigated. In free vibration analysis, non-dimensional natural frequency of FGPM plate initially decreasing considerably and then remaining almost constant with the increase in volume fraction index when material property graded by power law. When material properties are varied by sigmoid law, with an increase in volume fraction index, the non-dimensional natural frequency of FGPM plates remains virtually constant. FGPM plates have a lower non-dimensional natural frequency if the thickness to width ratio is greater. Non-dimensional natural frequencies of Clamped-Clamped FGPM plates (C-C-C-C) are greater compared to Clamped-Free FGPM (C-F-C-F) and Simply Supported Free FGPM (S-F-S-F).

Automated summary

The first-order shear deformation theory (FSDT) was used to study the natural frequency response of functionally graded piezoelectric plates subjected to static electrical and mechanical strain. A monomorph model for a functionally graded piezoelectric plate with material properties changing according to sigmoid law with respect to plate thickness was considered. A three-dimensional finite element model with a free tetrahedral element mesh was created to investigate variations in the FGPM plate's free vibration boundary conditions, composition, and geometry. The non-dimensional natural frequency of FGPM plates initially decreases considerably and then remains almost constant with an increase in volume fraction index when material property is graded by power law. When material properties are varied by sigmoid law, the non-dimensional natural frequency remains virtually constant with an increase in volume fraction index. FGPM plates have a lower non-dimensional natural frequency if the thickness to width ratio is greater. Clamped-Clamped FGPM plates (C-C-C-C) have higher non-dimensional natural frequencies compared to Clamped-Free FGPM (C-F-C-F) and Simply Supported Free FGPM (S-F-S-F).