Investigation of moderately large amplitude effect on nonlinear free vibrations of porous cylinders using multiple scale method

This study focuses on the nonlinear free vibrations analysis of porous cylindrical shells for general porosity distribution through thickness. The motion equations which are a system of four coupled nonlinear partial differential equations are extracted in the framework of Mirsky–Herrmann’s shear deformation theory and nonlinear von Karman relations. By employing the multiple-scale method, the system of equations is solved and an analytical solution is proposed for different orders of the equations. By utilizing a parametric study, the effect of different parameters on the nonlinear free vibration behavior of the porous cylinder is discussed. Moreover, the effect of different combinations of boundary conditions and different types of porosity distributions on the linear/nonlinear frequencies is studied. The results are compared with other references in the special cases. The nonlinear frequency behavior of porous cylinders may be hardening or softening and it depends on different conditions, for example, the porosity distribution and boundary conditions. The porosity affects significantly the natural frequency, allowing for substantial weight reduction without compromising frequency in certain cases.