Nonlinear forced vibration analysis of two-directional functionally graded truncated conical shells

It is crucial to comprehend the nonlinear vibration behavior of sophisticated engineering constructions to aid in the examination, creation and production procedures. The primary objective of this study, therefore, is to focus on exploring the nonlinear forced vibrational characteristics of two-directional functionally graded (TDFG) cone-shaped shell for the first time. To accomplish this, the motion equations of the TDFG cone-shaped shell are derived based upon the framework of first-order shear deformation theory (FSDT) in conjunction with von Kármán assumption. TDFG cone-shaped shell models have mechanical properties that can change smoothly and continuously across the thickness and length of the shell, following a power law distribution pattern. To discretize the partial differential equations and transform them into ordinary differential equations, the Galerkin approach was used and ultimately, these equations were solved using the multiple time scales method. The accuracy and effectiveness of this 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 behavior of the shell, highlighting the significant influence of transverse and longitudinal gradient indices on the nonlinear frequency response, which is not considered before. The new insights gained from this research could serve as valuable benchmark outcomes as well as contribute to a more comprehensive understanding of the nonlinear vibrations in future analysis and design processes. © 2024 World Scientific Publishing Company.