Flexural wave propagation in infinite beams on a unilateral elastic foundation

The problem of flexural wave propagation on a beam resting on a unilateral elastic substrate is addressed. The Euler–Bernoulli beam theory, which is valid for slender beams and for large enough wave length, is used. The governing equations are recalled, and the boundary conditions corresponding to the “single wave” periodic solutions are determined. The ensuing system of three algebraic transcendental equations is solved, and the exact solution of the problem is provided, in spite of the nonlinearity due to the piecewise behavior of the soil. The wave velocity as function of the foundation stiffness is obtained and compared with the classical case of the bilateral foundation. The main wave propagation properties are discussed, and some of them are illustrated with graphs reporting wave shapes.