Free Vibrational Response of Single-Layered Graphene Sheets Embedded in an Elastic Matrix using Different Nonlocal Plate Models
In this paper, the small scale effects are incorporated into the free vibration analysis of single-layered graphene sheets (SLGSs) embedded in an elastic medium. To this end, Eringen’s nonlocal elasticity continuum are applied to the different types of plate theory namely as the classical plate theory (CLPT), first order shear deformation theory (FSDT), and higher order shear deformation theory (HSDT). Winkler and Pasternak foundation models used to simulate the surrounding elastic medium are compared with each other. Explicit expressions are derived to calculate the natural frequencies of square SLGSs corresponding to each type of nonlocal plate model. Selected numerical results are given to indicate the influence of the nonlocal parameter, Winkler and Pasternak elastic moduli, mode number, and the side length of SLGSs in detail. Also, comparison is made between the vibrational responses of SLGSs obtained through different nonlocal plate theories. It is found that the elastic foundation and value of nonlocal parameter have quite significant effects on the natural frequencies of SLGSs and these effects are influenced by mode number as well as side length.