Periodic wave propagation in nonlocal beams resting on a bilinear foundation

The free wave propagation of periodic flexural waves on an infinite elastic Euler–Bernoulli nonlocal beam embedded in bilinear Winkler-type foundation is investigated. A general formulation of the elastic potential energy leads to a nonlinear nonlocal model with spatial derivatives up to the sixth order. The effect of the nonlocal parameters and of the different soil stiffnesses on the dynamical characteristics of the system is critically discussed. An enrichment of the system response with respect to the local beam is unveiled, and the crucial role played by the sixth-order nonlocal term is highlighted.