Thermomechanical vibration analysis of FGM viscoelastic multi-nanoplate system incorporating the surface effects via nonlocal elasticity theory

This paper deals with thermomechanical vibration analysis of multi nanoplate system based on nonlocal elasticity theory of Eringen. Each plate is assumed to be made of viscoelastic and functionally graded materials, also a visco-Pasternak medium joins them to each other. The material characteristics of each FGM nanoplates are assumed to be varied continuously across the plate thickness according to the power law function. By taking into account the surface effects, equations of motion are extracted via Hamilton’s principle and detailed derivations are presented. Numerical and analytical solutions are compared to each other to clarify the reliability of the presented method. Results are obtained for two kinds of chain conditions, namely, “Clamped-Chain” and “Free-Chain”. Finally, attention is focused on considering the influences of various parameters on vibrations of system such as thermal changes, nonlocal parameter, surface effects and properties of visco-Pasternak foundation and it is clearly demonstrated that these factors highly affect on vibration behavior.