Abstract
This paper investigates wave propagation of size-dependent functionally graded (FG) nanobeams resting on elastic foundation subjected to axial magnetic field based on the nonlocal strain gradient theory and Euler–Bernoulli beam model by using an analytical approach. The nonlocal beam model has a length scale parameter and captures the size influences. Material properties are spatially graded according to sigmoid distribution. A derivation of the governing equations for the wave propagation analysis of nanoscale S-FGM beams is conducted. Then, the dispersion relations between wave frequency and phase velocity with the wave number is investigated. It is found that wave propagation characteristics of nonlocal S-FGM beams are influenced by various parameters including length scale parameter, material graduation, elastic foundation parameters and magnetic field intensity.
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