A comprehensive study on the critical damping characteristics of vibrating functionally graded sandwich plates with general visco-Winkler–Pasternak foundations

In this study, a general visco-Winkler–Pasternak foundation will be created to analyze the vibrations of functionally graded sandwich plates. The visco-Winkler–Pasternak foundations serve as the base for the suggested viscoelastic foundation, which takes into account a new damping coefficient related to the shear layer’s shear interactions. The new viscoelastic foundation model can be easily reduced to other well-known visco- and elastic foundation models. Establishing the governing equations of motion is achieved using the simple higher-order shear deformation theory and Hamilton's principle. Applying analytical solutions to these equations involves solving them with different boundary conditions. The proposed model is validated through some comparison studies. To demonstrate the effects of certain parameters on the vibration behaviors of functionally graded sandwich plates resting on general visco-Winkler–Pasternak foundations, a parametric study is performed. The numerical results section presents some novel findings and emphasizes the importance of two damping coefficients on plate vibration behaviors.