LAUSR

Abstract The dynamic response of periodically restrained flexural structures, modeled as Euler–Bernoulli beams supported by flexible and dissipative supports at equally spaced points, to moving loads is investigated. Bloch–Floquet theorem and modal analysis are used to examine the dispersion relation and band structure of the infinitely long periodic beam and the frequency spectrum of the finite beam, respectively. It is shown that the natural frequencies of the finite beam fall within the propagation bands of the corresponding infinite beam and get closer to each other as the number of spans increases ultimately covering the propagation bands. The dynamic response to moving load is obtained via a novel method based on Floquet transformation in the frequency domain for infinite periodic beams and through modal summation for finite periodic beams. Through numerical examples, the effect of boundary conditions, e.g. support stiffness and damping, and the impact of moving load speed on the flexural response as well as the energy stored and dissipated within the supports are discussed.