Propagation of periodic waves in beams on a bilinear foundation

The propagation of periodic flexural waves in an Euler-Bernoulli beam resting on a bilinear elastic foundation is investigated. Although the problem is nonlinear, the closed form solution is obtained thanks to its piecewise linear nature. The dependence of the phase velocity on the two stiffnesses of the substrated is investigated in depth, and it is shown that a very complex behaviour is observed when the stiffnesses are large. Veering-like phenomena has been discovered, apparently for the first time. It is shown that some branches end with cusp points, not related to classical bifurcations. The stability of the considered waves is also addressed, in a restricted class of perturbations.