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This work examines how mass attachments that vary with time influence the motion of flexible pylons undergoing ground-induced vibrations. Specifically, an analytical solution is derived for a time-dependent, lumped mass attachment placed at the top of a cantilevered pylon undergoing time-harmonic longitudinal vibrations. At first, the solution to the governing equation of motion entails the recovery of the eigenvalue problem in the presence of a fixed mass. This is then followed by a generalization of this solution to allow for mass variability with time. It is noted that modal analysis no longer yields an uncoupled system of equations for the generalized coordinates, this necessitating a second step modal analysis, which is complicated by the fact that the system matrices are now time dependent. Results are presented in terms of time histories and frequency plots for the pylon displacement amplitude at the top, resulting from harmonic base motion of unit amplitude. The aim is to identify the frequency range over which the presence of a time-varying mass is either beneficial or detrimental in minimizing the pylon's kinematic response. Since the rate of change of the mass can be either positive or negative, the special cases of constant mass and of no mass can be recovered from the solution. Finally, this methodology can be generalized to include transverse and rotational vibrations of flexible pylons.

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In this work, we investigate the transient response of a model bridge traversed by a heavy mass moving with constant velocity. Two response regimes are identified, namely forced vibrations followed by free vibrations as the moving mass goes past the far support of the simply supported span of the bridge. Despite this being a classical problem in structural dynamics, there is an implicit assumption in the literature that moving loads possess masses that are at least an order of magnitude smaller than the mass of the bridge span that they traverse. This alludes to interaction problems involving secondary systems, whose presence does not alter the basic characteristics of the primary system. In our case, the dynamic properties of the bridge span during the passage of a heavy mass change continuously over time, leading to an eigenvalue problem that is time dependent. During the free vibration regime, however, the bridge recovers the expected dynamic properties corresponding to its original configuration. Therefore, the aim here is the development of a mathematical model whose numerical solution is validated by comparison with experimental results recovered from an experiment involving a scaled bridge span traversed by a rolling mass. Following that, the target is to identify regions in the transient response of the bridge span that can be used for recovering the bridge’s dynamic properties and subsequently trace the development of structural damage. In closing, the present work has ramifications in the development of structural health monitoring systems applicable to critical civil engineering infrastructure, such as railway and highway bridges.

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