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Nonlinear vibration of FGM sandwich doubly curved shallow shells reinforced by FGM stiffeners subjected to mechanical and thermal loading are investigated based on the first-order shear deformation theory (FSDT) with von Karman type nonlinearity, taking into account initial geometrical imperfection and smeared stiffener technique. Four material models of the FGM sandwich shells are presented. Explicit expressions for natural frequencies, nonlinear frequency-amplitude relation, and time-deflection curves of the FGM sandwich shallow shells are derived using Galerkin method.

Nonlinear vibration of functionally graded material sandwich doubly curved shallow shells reinforced by FGM stiffeners. Part 1: Governing equations