An eigenvalue solution for nonlocal vibration of guide supported perfect/imperfect functionally graded power‐law and sigmoid nanobeams on one‐parameter elastic foundation

Abstract To the best of the authors' knowledge, this study for the first time, proposes a finite element (FE) model to investigate the size‐dependent vibrational responses of guide supported imperfect functionally graded (FG) nonlocal beams embedded in an elastic foundation in the context of nonlocal elasticity theory (NET). The main objective of this paper is to present a nonlocal FE solution for vibration analysis of imperfect FG nanobeams including nonlocal effect, power‐law distribution function, sigmoid distribution function, even porosity model, uneven porosity model, elastic foundation parameter, and guide support condition. It is considered that perfect/imperfect FG nanobeams are made of silicon carbide (SiC) and aluminum (Al) and that beam properties vary along the height direction. In addition, the nanobeams rest on a one‐parameter elastic foundation and this foundation provides the interaction between the structure and the soil with elastic springs. The frequency values of perfect/imperfect FG power‐law and sigmoid nanobeams obtained by using a nonlocal FE method are shown via tables and figures.