ABSTRACT
In this chapter of the book, the mathematical representation of the wave propagation problem will be rewritten for the cases in which the nanostructure is embedded in an elastic or viscoelastic medium. The effects of three types of foundation will be included in the analysis. The first one is Winkler-type medium, the second one is the Pasternak-type medium, and the last one, which is a viscoelastic one, is the visco-Pasternak-type medium. The constituent material used in Chapter 4 will be selected, and the small-scale effects will be included within the framework of the nonlocal strain gradient based elasticity. Once the eigenvalue equation of the problem is solved, it can be concluded that elastic coefficients of medium (i.e., either Winkler or Pasternak coefficient) can amplify the dynamic responses of the system, whereas the responses can be damped by adding the damping coefficient of the medium.
