Vibration Analysis of Partially Supported Porous Functionally Graded Cylindrical Shells on the Winkler Elastic Foundation with General Boundary Conditions

This study investigates the free vibrational analysis of cylindrical shells made of Porous Functionally Graded Materials (PFGMs) under arbitrary boundary conditions. To present more general formulations, it is assumed that the cylinder is partially bounded by an elastic foundation, characterized by either constant or variable stiffness. Utilizing the Firstorder Shear Deformation Theory (FSDT) and applying the Hamilton's principle, the governing differential equations of motion have been obtained. An analytical solution i.e. Rayleigh-Ritz method combined with Lagrange multipliers has been used to solve these equations. It is worth noting that the inclusion of a partially elastic foundation results in the coupled equations between the cylinder's length and angular directions, which is addressed through the series-solution. After validating the results for different boundary conditions and porosity types, we proceed to explore the influence of porosity function, boundary conditions, geometric parameters, and elastic foundation on the free vibrational characteristics. This comprehensive analysis provides insights into the behavior of PFGMs cylindrical shells, aiding in the design and optimization of structures utilizing these materials.