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This article investigates the nonlinear vibration behavior of multiscale nanocomposites nanoshell subjected to hygrothermal environment and resting on elastic foundations. The novelty and contribution of this article is considering a multiscale doubly curved sandwich nanoshell. Three-phase composite nanoshell composes of polymer-Carbon nanotube-fiber (PCF) and polymer-Graphene platelet-fiber (PGF) according to Halpin-Tsai model. Various distributions patterns such as U (uniform), X, A and O are considered. The classical shell theory and nonlocal strain gradient theory including von Kármán strain–displacement relationships are employed to build the size-dependent governing equations. The governing equations of multiscale nanoshell have been implemented by Hamilton's principle and solved by homotopy perturbation method. For investigating correctness and accuracy, this paper is validated by other previous researches. Finally, the effects of different parameters such as temperature rise, various distributions patterns and curvature ratio have been investigated. • Nonlinear vibration behavior of multiscale nanocomposites nanoshell is investigated in hygrothermal environment. • The influence of different parameters such as temperature rise, various distributions patterns, curvature ratio are investigated in detail. • Various distributions patterns such as U (uniform), X, A and O are considered. • Via the classical shell theory and the von Kármán type hypothesis the displacements are expressed. • Nonlocal strain gradient governing equations of multiscale nanoshell have been implemented by employing the Hamilton's principle. • Using the homotopy perturbation method, the equations of motions are solved. • The governing equations of multiscale shell have been derived by implementing Hamilton's principle. [ABSTRACT FROM AUTHOR]

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]