Determination of dynamic gradient elasticity length scales

Abstract

Wave dispersion is a widely recognised phenomenon that occurs when elastic waves propagate through a heterogeneous microstructured material; reflection and refraction of higher frequencies leads to an apparent reduction of the wave speed with frequency. Enhanced continua are frequently employed to capture this phenomenon efficiently. Numerical experiments are performed in this paper to establish a procedure for the determination of the length scale parameters used in dynamic gradient elasticity using spectral analysis. Suitable values of the length scale parameters are determined and verified for a one-dimensional laminated bar and for a two-dimensional chequerboard plate.