Free vibration analysis of functionally graded porous materials complex shells with variable thickness

This research investigates the vibration characteristics of composite shells featuring a cylindrical-hemispherical geometry, fabricated from functionally graded porous materials with varying thicknesses. Two kinds of boundary conditions are assumed: the first assumes both ends are free, while the second involves clamped and free edges for the cylindrical and hemispherical sections, respectively. The analysis employs three-dimensional elasticity principles in conjunction with the Ritz method, utilizing orthogonal polynomials like Legendre polynomials as admissible functions. The natural frequencies' convergence is demonstrated, and results are validated against prior findings from finite element and analytical methods. After confirming the model's accuracy, the influence of porosity is examined. The results indicate that a higher percentage of porosity leads to a decrease in the shell's natural frequencies. The study also investigates how natural frequencies are affected by various geometric parameters. Ultimately, the outcomes highlight the significant impact of porosity and geometric attributes on the frequencies of porous shells. Additionally, torsional and axisymmetric vibration modes are observed to be more influential under clamped-free conditions than under free-free conditions. A general trend of decreasing frequencies with reduced thickness is identified, and higher porosity levels, leading to lower stiffness, consistently reduce frequencies across all modes.