Nonlinear free and forced vibration analysis of multiscale composite doubly curved shell embedded in shape

In this research, nonlinear free and forced vibration behaviors of the multiscale doubly curved composite shells have been investigated. By using Reddy's third-order shear deformation theory (TSDT) and von-Karman type nonlinearity the strains and stresses are obtained. Three-phase composites shells with polymer/carbon nanotube/fiber and polymer/graphene platelet/fiber and shape-memory alloy (SMA)/matrix according to the Halpin–Tsai model have been analyzed. The governing equations of composite shell have been derived by implementing Hamilton's principle, and according to the multiple scales perturbation method have been solved. The obtained results are validated through the comparison with the available results. Finally, the effects of different parameters such as volume fraction of SMA, temperature rise, various distributions pattern, aspect, and curvature ratio considered on nonlinear frequency have been studied. The results indicate that the changes of the fundamental vibrational mode shape have a significant influence on the nonlinear frequency of the composite shell