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• Effects of heating and cooling thermal shock on thermally induced vibration (TIV) are explored. • Influence of geometric nonlinearity under heating/cooling thermal shock forms is revealed. • The TIV characteristics of sandwich beams with auxetic honeycomb cores are discussed and compared with traditional honeycomb. • The instability conditions of the clamped beam with immovable ends under heating thermal shock are given. The nonlinear thermally induced vibration (TIV) characteristics of sandwich beams with auxetic honeycomb cores under general boundary conditions are studied. Based on first-order shear deformation theory, the dynamic governing equations are obtained through Hamilton principle, in which geometric nonlinearity and temperature dependence are considered. The temperature field along the thickness is calculated by finite element method and nonlinear TIV responses are solved via Newton-Raphson-Newmark method. The effects of temperature dependency, thermal shock forms, geometric nonlinearity, thicknesses of beam and face-sheet, boundaries and honeycomb geometrical parameters are studied. Results show that the reduction of the absolute inclined angle of the auxetic honeycomb can weaken the TIV responses. The influence of geometric nonlinearity on quasi-static and dynamic responses depends on the thermal shock form. Thermal buckling is the necessary condition for the occurrence of the TIV in clamped beams with immovable ends. Moreover, the research provides some design references to suppress the TIV responses of the sandwich beam with auxetic honeycomb core. [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]