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The aims and objectives of the current study are to investigate the vibration analysis of the graphene sheet with attached spring, mass, and damper system for the first time. For this purpose, the governing equation is derived employing Hamilton’s principle regarding the nonlocal Eringen theory. The graphene sheet is supposed to be rested on a Winkler elastic foundation. Galerkin’s method is being used to obtain frequency on various boundary conditions. To validate our work, the proposed model is demonstrated by comprising the present model with the results available in the literature. The influence of different parameters such as the attached mass, nonlocal parameter, aspect ratio, and Winkler foundation of a graphene sheet on the non-dimensional vibration frequencies are presented in detail. The results indicate that adding the spring-mass system leads to an increase in the non-dimensional frequency parameter. The outcomes of this survey can be utilized in the construction of biological and chemical nanosensors.

Size-dependent vibration behavior of graphene sheet with attached spring-mass and damper system based on the nonlocal Eringen theory