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Modern engineering extensively employs complexly curved shell structures, presenting mathematical challenges in analyzing their mechanical behavior due to geometric intricacies. The recent trend of incorporating advanced lightweight materials into these structures drives the need to develop improved theories and methods. This study presents an investigation into the free vibration analysis of barrel-shaped sandwich (BSS) shells using a modified thick shell theory (MTST). These sandwich shells feature functionally graded (FG) ceramic-metal layers on both inner and outer surfaces, with a lightweight honeycomb core. Notably, the honeycomb layer's thickness surpasses that of the inner and outer layers, necessitating the application of thick shell theory for accurate analysis. However, previous studies have often used classical theories for thin shells, and those applying thick shell theory sometimes neglected the curvature effects in the fundamental equations and rotary inertia components. Thus, this research employs the MTST to overcome these limitations. The study includes comparative validations and explores the impact of material parameters and curvature radii on the natural frequencies of these barrel-shaped sandwich shells through numerical examples. [ABSTRACT FROM AUTHOR]

In this study, a model for the nonlinear dynamic analysis of the geometrically imperfect sandwich beam with functionally graded material (FGM) facets and auxetic honeycomb core is proposed. The auxetic feature of the honeycomb material is realized by a homogenization method, which gives the expressions of the effective material coefficients in terms of material property and cellular geometric parameters. The nonlinear motion equation of the geometrically imperfect beam is derived based on the Reddy's higher shear deformation theory, von Kármán nonlinear theory, as well as general geometric imperfection function. The thermal effect on the material properties and structural rigidity is also taken into account in this model. The Newmark method and Newton–Raphson iterative method are employed to solve the nonlinear motion equation of the sandwich beam. In numerical examples, the dynamic response of the sandwich beam under two types of load, i.e. moving load and impulse load, are discussed in details. The influences of various factors (such as material parameter, geometric imperfection, and thermal condition) on the nonlinear dynamic behaviors of the sandwich beam are elaborately investigated. The numerical results show those factors can play significant roles in the bearing ability, structural stiffness, or nonlinear dynamic behaviors of the sandwich beam in certain conditions. Some key conclusions on the influences are drawn from the numerical results, which can be a useful reference for future investigations. [ABSTRACT FROM AUTHOR]