ABSTRACT
This chapter deals with the application of the size-dependent continuum-mechanics-based theories in the determination of the wave propagation curves of nonhomogeneous functionally graded material nanobeams and nanoplates. The mathematical formulation of the problem for both nanobeam and nanoplate will be organized on the basis of the definition of the Hamilton’s variational principle. Classical and shear deformable beam and plate models will be used for the purpose of deriving the governing equations. Two methods of material homogenization will be explained to cover the dependency of the material properties of the composite material on the thickness direction. Finally, the problems considered will be solved via analytical solutions introducing exponential solution functions for the displacement fields and considering the wave number and frequency of the scattered waves. The results of this chapter reveal the completely different effects of a material’s length-scale and nonlocal parameters on the determination of the scale-dependent wave propagation responses of nanostructures.
