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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]

An analytical framework has been developed for predicting the equivalent in-plane elastic moduli (longitudinal and transverse Young’s modulus, shear modulus, Poisson’s ratios) of irregular auxetic honeycombs with spatially random variations in cell angles. Employing a bottom up multi-scale based approach, computationally efficient closed-form expressions have been derived in this article. This study also includes development of a highly generalized finite element code capable of accepting number of cells in two perpendicular directions, random structural geometry and material properties of irregular auxetic honeycomb and thereby obtaining five in-plane elastic moduli of the structure. The elastic moduli obtained for different degree of randomness following the analytical formulae have been compared with the results of direct finite element simulations and they are found to be in good agreement corroborating the validity and accuracy of the proposed approach. The transverse Young’s modulus, shear modulus and Poisson’s ratio for loading in transverse direction (effecting the auxetic property) have been found to be highly influenced by the structural irregularity in auxetic honeycombs. [ABSTRACT FROM AUTHOR]