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This is the first research on the nonlinear vibration of smart viscoelastic composite doubly curved sandwich shell with flexible core and MR layers with different distribution patterns. By using Reddy's third order shear deformation theory (TSDT), the strains and stresses are obtained. This smart model including multiscale composite layers, flexible core and magnetorheological layer (MR). According to the Halpin-Tsai model three-phase composites layers have been considered. The governing equations of the multiscale doubly curved shell have been derived by implementing the Hamilton's principle. For investigating correctness and accuracy, this paper is validated by other previous studies. The results of this work are validated through the comparison with the results available researches. Finally, the influence of different parameters such as temperature rise, various distributions pattern, magnetic fields, and curvature ratios on nonlinear frequency response are investigated in the details. The results presented that the multiscale doubly curved sandwich shell with flexible core show a complex behavior. [ABSTRACT FROM AUTHOR]

This is the first research on the nonlinear vibration analysis of composite sandwich doubly curved shell with a flexible core integrated with a piezoelectric layer. By using the higher order shear deformable theory (HSDT) for the face sheets and the third-order polynomial theory for the flexible core, the strains and stresses are obtained. It is assumed a smart model including multiscale composite layers shell with a flexible core and magnetorheological layer (MR) that leading up by the nonlinearity of the in-plane and the vertical displacements of the core. Three-phase composites shells with polymer/Carbon nanotube/fiber (PCF) and polymer/Graphene platelet/fiber (PGF) and Shape Memory Alloy (SMA)/matrix either according to Halpin-Tsai model have been considered. The governing equations of multiscale shell have been derived by implementing Hamilton's principle and solved by multiple scale method. For investigating the correctness and accuracy, this paper is validated by other previous researches. Finally, the effect of different parameters such as temperature rise, various distributions pattern, magnetic fields and curvature ratio are explored in detail. [ABSTRACT FROM AUTHOR]