Memory effects in wave propagation

This paper investigates the response of structures including in their constitutive relationship memory effects. The analysis is carried on both by using modal analysis and a wave approach. Memory effects appears by a convolution integral added to conventional differential terms. The dispersion relation for an infinite waveguide is obtained together with the frequency response function for its finite counterpart, with given boundary conditions. The analysis shows large modifications of the wave propagation characteristics in the low frequency range, both for phase and group velocity, and an associated displacement of the structure natural frequencies.