Nonlinear vibrations analysis of two-directional functionally graded porous cylindrical shells resting on elastic substrates in a thermal environment based on Donnell nonlinear shell theory

The primary objective of this study is to investigate the nonlinear free vibrational characteristics of temperature-dependent two-directional functionally graded porous (TDFGP) cylindrical shells resting on elastic substrates in a thermal environment. To accomplish this, the thermomechanical equations are derived based on the Donnell nonlinear shell theory framework in conjunction with the von Kármán assumption. Two-directional functionally graded porous cylindrical shell models have mechanical properties that can change smoothly and continuously across the length and thickness of the shell. Additionally, it is assumed that the internal porosities in the matrix materials can be dispersed into two independent patterns, either even or uneven porosity distribution. The nonlinearity in free vibration assessed via the nonlinear-to-linear frequency ratio concerning the central deflection amplitude can be gained employing the Galerkin discretization approach and modified Poincare–Lindstedt (P-L) method. The accuracy and effectiveness of the present analytical model are indicated through comparison with existing solutions. Finally, some comprehensive parametric investigations are carried out to gain insight into the impacts of several factors on the nonlinear free vibration characteristics of structures under different conditions. The results of this article demonstrate that parameters such as gradient indices, volume fraction, distribution pattern of porosity, geometric parameters, and ambient temperature rise significantly influence the structure’s nonlinear frequency and free vibration response.