Large-amplitude nonlinear vibrations characteristics of bi-directional functionally graded plate having microstructure defects in hygro-thermal environment

The present article investigates the nonlinear hygro-thermal vibration characteristics of bi-directional functionally graded plates (BFGP) with microstructural defects. The distribution of material properties is anticipated to vary gradually along both thickness and length directions according to the modified power-law distribution. A novel expression has been developed to solve for the nonlinear temperature variation along the thickness of the BFGP. The micro-structural defects in terms of porosity have been incorporated in the formulation using a newly developed porosity model for a BFGP. A refined non-polynomial trigonometric higher-order shear deformation theory (HSDT) with a von Karman sense of geometric nonlinearity has been employed for the vibration response of BFGP. The finite element formulation has been carried out utilizing the C⁰ continuous Lagrangian quadrilateral element with nine nodes and eight degrees of freedom per node. The equations of motion have been derived using a variational approach. Various validation and comparative studies have been conducted to substantiate the current formulation's authenticity. The effect of the geometric nonlinearity, boundary constraints, volume fraction index along thickness (n) and volume fraction index along length (q), porosity index, temperature, and moisture concentration difference on the vibration frequency ratios (VFR) has been covered in depth. The VFR is more sensitive to the volume fraction indices (VFI) ' n′ than 'q'. Incorporating porosity decreases the VFR of BFGP, but it increases at higher amplitude ratios when BFGP becomes more porous. The VFR of BFGP exhibits nonlinear behavior with increasing moisture concentration and also varies non-linearly with the rise in amplitude ratio due to the hygro-thermal environment.