Abstract
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.
Published Version
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