A general viscoelastic foundation model for vibration analysis of functionally graded sandwich plate with auxetic core

Abstract

This study presents a significant advancement in the vibration analysis of functionally graded sandwich plates with auxetic cores by introducing a general viscoelastic foundation model that more accurately reflects the complex interactions between the plate and the foundation. The novelty of this study is that the proposed viscoelastic foundation model incorporates elastic and damping effects in both the Winkler and Pasternak layers. To develop the theoretical framework for this analysis, the higher-order shear deformation theory is employed, while Hamilton's principle is used to derive the governing equations of motion. The closed-form solution is used to determine the damped vibration behaviors of the sandwich plates. The precision and robustness of the proposed mathematical model are validated through several comparison studies with existing numerical results. A detailed parametric study is conducted to investigate the influence of various parameters, including the elastic and damping coefficients of the foundation, the material gradation, and the properties of the auxetic core on the vibration behavior of the plates. The numerical results provide new insights into the vibration characteristics of sandwich plates with auxetic cores resting on viscoelastic foundation, highlighting the significant role of the two damping coefficients and auxetic cores in the visco-vibration behavior of the plates.