On nonlinear vibration and snap-through buckling of long FG porous cylindrical panels using nonlocal strain gradient theory

Abstract

In the current research, nonlinear vibration and snap-buckling analysis of long cylindrical panels made of functionally graded (FG) porous materials are studied. The case of cylindrical panels with shallow curvature and long length is analyzed using an approximate nonlocal strain gradient model. Non-homogeneous properties of the cylindrical panel with uniform distributed porosities are graded across the thickness. The interaction of the cylindrical panel with a nonlinear elastic foundation is also included into the formulation. The mathematical formulations are expressed based on the high-order shear deformation theory and the Donnell kinematic assumptions. Three nonlinear motion equations of the cylindrical panel are established by employing the Hamilton principle. These coupled partial differential equations are analytically solved for the case of long cylindrical panels which is immovable pinned on both straight edges. The two-step perturbation technique and Galerkin’s method are implemented to extract the nonlinear free vibration and snap-buckling characteristics of the shell. The natural frequencies and load-deflection curves are first validated for the cases of long plates and shells. Afterwards, novel parametric studies are developed to show the effects of nonlocal and length scale parameters, power law index, porosity coefficient, foundation components, and the geometrical parameters of the shell.