Effects of the Strain Gradients on the Band Structures of the Elastic Waves Propagating in 1D Phononic Crystals: an Analytical Approach

•The effects of strain gradients on the frequency band-gap characteristics are discussed in 1D nano-sized PCs.•The strain gradients may significantly influence the frequency band structures of the elastic waves propagating.•An analytical solution based on the transfer matrix method is employed.•The effects of small-scale parameters in strain-gradient theory on the frequency dispersion curves are discussed.