Nonlinear vibration behavior of functionally graded porous cylindrical panels

The paper presents large amplitude free vibration response of functionally graded porous (FGP) cylindrical panels considering different shell theories and boundary conditions. Nonlinear governing equations are obtained based on two shell theories, first order shear deformation theory (FSDT) and higher order shear deformation theory (HSDT). The von Karman geometrical nonlinearity along with the Hamilton principle is utilized. Mechanical properties of the open-cell foam are assumed to vary continuously through the thickness. This graded porosity offers a smooth stress distribution along the thickness of the panel. Generalized differential quadrature method (GDQM) is utilized to discretize the nonlinear dynamic governing equations along with three different boundary conditions. To solve the set of equations that include highly nonlinear parameters, the harmonic balance method along with the direct iterative approach is used. The results present the influence of geometrical parameters, vibration amplitude, porosity distribution, shell theories and boundary conditions on the nonlinear frequencies. It is found that both porosity distribution and porosity coefficient have a remarkable effect on the nonlinear natural frequencies of FGP cylindrical panel. To enhance the dynamic response of the cylindrical panel, porosity should be avoided near the panels' surfaces.