Exact solution for thermal vibration of multi-directional functionally graded porous plates submerged in fluid medium

Abstract

An analytical method for analyzing the thermal vibration of multi-directional functionally graded porous rectangular plates in fluid media with novel porosity patterns is developed in this study. Mechanical properties of MFG porous plates change according to the length, width, and thickness directions for various materials and the porosity distribution which can be widely applied in many fields of engineering and defence technology. Especially, new porous rules that depend on spatial coordinates and grading indexes are proposed in the present work. Applying Hamilton’s principle and the refined higher-order shear deformation plate theory, the governing equation of motion of an MFG porous rectangular plate in a fluid medium (the fluid-plate system) is obtained. The fluid velocity potential is derived from the boundary conditions of the fluid-plate system and is used to compute the extra mass. The Galerkin-Vlasov solution is used to solve and give natural frequencies of MFG porous plates with various boundary conditions in a fluid medium. The validity and reliability of the suggested method are confirmed by comparing numerical results of the present work with those from available works in the literature. The effects of different parameters on the thermal vibration response of MFG porous rectangular plates are studied in detail. These findings demonstrate that the behavior of the structure within a liquid medium differs significantly from that within a vacuum medium. Thereby, they offer appropriate operational approaches for the structure when employed in various mediums.

Keywords

• Plate-fluid contact
• Galerkin Vlasov’s method
• Multi-directional functionally graded plate
• Novel porosity
• Thermal vibration
• Refined higher-order shear deformation theory