On the response spectrum of Euler–Bernoulli beams with a moving mass and horizontal support excitation

In this study, the response spectrum of a time-varying system such as a beam subjected to moving masses under a harmonic and earthquake support excitations is explored. The excitations are supposed to act on the horizontal directions of the beam axis. The inertial effect of the moving masses on the natural frequencies of the beam for different cases of loading is investigated and a critical value of a so called parameter “mass staying time” is presented to avoid dynamic instability of the system. Finally, some 3D response spectra for different supports excitations as well as the beam natural frequencies are depicted.

► The response spectrum of a time-varying system such as a beam subjected to moving masses under a harmonic and earthquake support excitations is explored.
► The effect of mass velocity is investigated on the resonance frequency of the system.
► A so called parameter “mass staying time” is presented to study the mass velocity effect on the system frequency.
► This subject is useful to define the predominant and resonant frequencies of bridges under the effect of traveling vehicles.