A meshless collocation method for band structure simulation of nanoscale phononic crystals based on nonlocal elasticity theory.

• A meshfree LRBFCM based on the nonlocal elasticity theory is developed for wave propagation analysis in nanoscale phononic crystals. • The band structures of 1D nanoscale phononic crystals obtained by the LRBFCM agree well with the reference results. • The band structures and transmission coefficients of elastic waves in 2D nanoscale phononic crystals are computed and analyzed by the LRBFCM. In this paper, the band structures of nanoscale phononic crystals based on the nonlocal elasticity theory are calculated by using a meshfree local radial basis function collocation method (LRBFCM). The direct method is applied to enhance the stability of the derivative calculations in the LRBFCM. A simple summation in the LRBFCM is proposed to deal with the integration related to the nonlocal stresses or tractions. The LRBFCM for the band structure calculations is validated by the results obtained with the first-principle and the transfer matrix (TM) method for one-dimensional (1D) phononic crystals, as well as the comparison of the frequency responses of the two-dimensional (2D) periodic structures. [ABSTRACT FROM AUTHOR]