Third-order isogeometric analysis for vibration characteristics of FGP plates in the thermal environment supported by Kerr foundation

This paper extends isogeometric analysis (IGA) based on third-order shear deformation theory (TSDT) for vibration analysis of functionally graded porous (FGP) plates in the thermal envi-ronment resting on Kerr foundation. IGA is based on non-uniform rational B-spline (NURBS) basic functions, so it can represent exact geometry and satisfy higher-order approximation (C1 continuous function) conditions of TSDT. This combination ensures high accuracy, including transverse shear deformation, without having to use any correction factors. The temperature field via the plate thickness satisfies the steady-state heat transfer equation. The governing equations are derived from Hamilton's principle. Then, numerical examples are conducted to validate the effectiveness of the proposed method. Finally, the effects of geometrical parameters, material properties, boundary conditions (BCs), temperature change and foundation stiffness on the thermal vibration of FGP plates are fully considered.

Automated summary

This paper extends the isogeometric analysis based on third-order shear deformation theory for vibration analysis of functionally graded porous plates in a thermal environment resting on Kerr foundation. The proposed method could accurately represent the geometry and satisfy higher-order approximation conditions, ensuring high accuracy without using any correction factors. The effectiveness of the method was validated through numerical examples, considering the effects of geometrical parameters, material properties, boundary conditions, temperature change, and foundation stiffness on the thermal vibration of FGP plates.