Interplay of porosity and viscoelasticity in nonlinear free vibrations of cylindrical shells

Abstract This study presents an analytical investigation into the nonlinear free vibrations of viscoelastic porous cylinders, accounting for the critical effects of geometrical nonlinearity. The nonlinear governing equations of motion are derived for an arbitrary porosity distribution using Hamilton’s principle, integrated with the first-order shear deformation theory and von Kármán nonlinear relations. The material’s viscoelasticity is modeled via the three-parameter Zener model, while the porosity effect is incorporated through Biot’s assumption. To resolve the complex nonlinear equations, the multiple-scale method is employed. A comprehensive parametric study is conducted to elucidate the influence of various porosity distributions, viscoelastic parameters, and geometric configurations on the natural frequencies. A significant advantage of the proposed analytical framework is its versatility in accommodating any continuous porosity distribution. The accuracy and reliability of the analytical results are rigorously validated through comparisons with existing literature and finite element analysis benchmarks.