Vibration analysis of bidirectional functionally graded (BDFG) nanobeams partially resting on elastic foundation

Vibration of bidirectional functionally graded (BDFG) nanobeams partially resting on elastic foundation is investigated in this paper. The material properties of the nanobeams are considered to vary in both axial and transverse directions by power gradation laws. The nonlocal elasticity theory considering the scale effect is employed in the derivation of governing equations. The finite element method is used to establish the discretized equation of motion and to predict the frequencies. The numerical results reflect the significant influence of the material gradation, the nonlocality parameter as well as the foundation on the vibration characteristics of the BDFG nanobeams.