Vibration of a periodically supported beam on an elastic half-space

The steady-state vibration of a periodically supported beam on an elastic h alf-space under a uniformly moving harmonically varying load is investigate d. The concept of equivalent stiffness of a half-space is used for problem analysis. It is shown that the half-space can be replaced by a set of ident ical springs placed under each support of the beam. The equivalent stiffnes s of these springs is a function of the frequency of the beam vibrations an d of the phase shift of vibrations of neighboring supports. It is found tha t the equivalent stiffness is equal to zero for some relationship between t he frequency and the phase shift. The reason for this is that the surface w aves generated by all supports can come to any support in phase, providing an infinite displacement. It is demonstrated that the equivalent stiffness has a real and an imaginary part. The imaginary part arises due to radiatio n of waves in the half-space. The expressions are derived for the steady-st ate response of the beam to the moving load. The limiting case of a constan t load is considered, showing that the load moving with the Rayleigh wave v elocity causes resonance in the system. (C) Elsevier, Paris.