On the solution of large‐amplitude vibration of carbon nanotube‐based double‐curved shallow shells

The article deals with the large‐amplitude vibration of carbon nanotube‐based double‐curved shallow shells (CNTBDCSSs). After mathematical modeling of CNTBDCSSs, the von Karman‐type nonlinear basic relations of CNTBDCSSs are created, and then the nonlinear equations of motion are derived. Using an extended mixing rule, the CNTBDCSSs are estimated approximately by introducing some performance parameters. Four different carbon nanotube distributions are considered. The nonlinear basic equations are solved applying superposition, Galerkin, and semi‐inverse methods; and the frequency–amplitude relation for the large‐amplitude vibration of CNTBDCSSs is obtained. The nonlinear frequency to linear frequency ratio of CNTBDCSSs is determined as a function of the amplitude. The results are compared with published results to check the reliability and accuracy of the proposed formulation. It follows a systematic investigation aimed at checking the sensitivity of the nonlinear response to some reinforcement parameters and geometry, as the distribution of CNTs within the matrix.