Finite element modeling of two-directional FGM beams under hygrothermal effect

This investigation describes the computational characteristics of two-directional functionally graded beams under the hygrothermal effect. A prismatic two-directional functionally graded beam (FGM) is used in this work. Temperature and moisture are applied to this FGM beam. Stainless steel (SUS304) and silicon nitride (Si₃N₄) are the materials used in their construction. Finite element method (FEM) software calculates the eigenfrequencies of two-directional FGM (COMSOL Multiphysics). The power law governs the material properties. The Euler–Bernoulli beam theory (EBT) is used in this study. The mechanical parameters are varied in longitudinal and transverse directions. The eigenfrequencies of two-directional FGM beams are affected by the material gradient parameter, the boundary condition, and the aspect ratio under the influence of the hygrothermal effect. The results obtained for reduced cases are used to validate the results computed with the FEM. The natural frequencies decrease with increased moisture concentration and temperature variation under clamped–clamped (C–C) boundary conditions and increase under clamped-free (C–F) boundary conditions. It is also observed that natural frequencies increase with the increase in material gradient parameters in the z-direction (n_z) and decrease with the increase in material gradient parameters in the x-direction (n_x) under C–C and C–F end conditions. With the increase in aspect ratio, the natural frequency increases under C–C and C–F boundary conditions.