Nonlinear vibration of functionally graded porous variable thickness toroidal shell segments surrounded by elastic medium including the thermal effect

The present study deals with the nonlinear vibration of functionally graded porous (FGP) variable thickness toroidal shell segments surrounded by elastic medium subjected to axial compression and external pressure, including the thermal effects. Three types of uniform, symmetric, and non-symmetric porosity distributions are considered. The improved Donnell shell theory with von-Karman nonlinearity, and Stein and McElman's assumptions are used to obtain the equations of motion of toroidal shell segments. The dynamic characteristics of shells such as natural frequencies and nonlinear frequency-amplitude relation are determined by using the solution in terms of displacements in conjunction with Galerkin's method. The present approach is validated by comparing with the available results for particular cases. Effects of geometrical characteristics, the porosity distribution types, the porosity coefficient, the thickness distribution parameter, temperature and pre-loaded static axial compression on the nonlinear vibration response of the FGP variable thickness convex and concave toroidal shell segments are studied in detail.