Generalized boundary continuous method for the free vibration solution of clamped porous plates

This article presents analytical closed-form solutions for the free vibration response of isotropic and porous plates with fully clamped (C4) boundary conditions. For the first time, the double Fourier series-based boundary continuous method (BCM) and the Carrera unified formulation (CUF) are used to obtain analytical solutions for the highly coupled partial differential equations of motion. The Taylor-like polynomials are employed within the CUF-based displacement field to accurately model the complex behavior of the plate along the thickness direction. The equations of motion and natural boundary conditions are derived by using the principle of virtual displacement (PVD). The BCM is employed to solve the governing equations yielding strong-form (exact in the limit) solutions. The validity and robustness of combining CUF and BCM are assessed by detailed comparison with 3D and 2D references available in the open literature and, where possible, with commercial software. The effects of the number of trigonometric terms m,n of the double Fourier series-based solution, side-to-thickness ratio b/h, porous distribution patterns, and porosity coefficient e0 on the accuracy and convergence characteristics of the proposed methodology are investigated. Finally, the proposed strategy of solution appears to be suitable for predicting the natural frequencies of structures using data-driven artificial intelligence.