Ritz Solution of Vibration Analysis of Functionally Graded Porous Elliptic Shells and Panels Under Various Arbitrary Boundary Types

This paper seeks to establish a generalized numerical model to examine the free vibration behavior of functionally graded porous (FGP) elliptical shells and panels with various boundary types. The model is built on first-order shear deformation theory (FSDT) to express structural displacements. A segmentation technique is used to maintain continuity between shell elements, and virtual spring boundary techniques are employed to simulate arbitrary boundaries. Variable-coefficient Jacobi polynomials are introduced as admissible functions for displacement. Finally, the Ritz variational method, combined with the least-squares weighted residual method (LSWRM), is used for constructing the energy functional and solving the energy equations. Validation of the numerical model against finite element and literature results confirms its reliability and convergence properties. This study also explores the effects of geometric parameters and boundary conditions on FG elliptical shells and panels, providing a theoretical basis for future research.