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In structural dynamics, loads having varying positions has been broadly studied. Such loads are so called moving loads which appears in various applications in industry. High speed machining systems, overhead cranes, cable ways, pavements, computer disc memories and robot arms are a few examples of moving load dynamic problems. Vibration of bridge structures subject to moving vehicles is often referred to as an application of moving load problems. A great number of researchers proposed numerical and analytical methods to deal with the vibration of solids and structures under travelling loads. A famous classic approach in the simulation of moving loads is the moving force. In moving force model, a constant traveling force is assumed to act upon the base structure. However, this assumption yields to reasonable structural analysis if the mass of the moving object is negligible. Nowadays, with ongoing advances of transportation technology, the mass, speed and acceleration of moving vehicles are notably increased. In this regard, during the last few decades, many researchers showed that the moving force is no longer valid for large moving masses. Therefore, the moving mass simulation has been proved to be closer to the physical model of vehicle bridge interaction. As a common practice, bridges carrying moving vehicles has been assumed as vibrating beams excited by point moving masses. It has been very customary to consider the midspan or center point of the base beam as the reference point in order to assess the maximum dynamic response of the structure under moving mass; therefore, most of the existing computed design envelopes are related to the values occurring at the midpoint of the structure. However, the location of the maximum values occurrence is not necessarily at midspan. To shed light on this issue, in this research an analytical-numerical method is established to capture dynamic response of an Euler-Bernoulli beam traversed by a moving mass. Most of the available literature on moving load problem is concerned with the travelling loads having constant speeds. To remove this restrictive presumption, in this paper, the considered moving mass is assumed to move at non-zero constant acceleration. The beam is considered to be undamped and initially at rest. The moving mass is assumed to maintain full contact condition with the base beam while sliding on it. By exploiting a series of continuous shape functions having time varying amplitude factors, a norm space is provided by which the beam spatial domain is discretized. The problem is then transformed into time domain for which a time integration method is utilized. Absolute maximum dynamic response of the supporting beam under the passage of accelerated moving mass is extensively sought over the beam length. In this manner, whole beam length is being monitored for the maximum values at each time step of time integration procedure. The beam absolute maximum dynamic response is comprehensively computed considering different mass ratios and extensive range of linearly time varying velocities. Parametric studies are carried out on the absolute maximum values of dynamic flexural moments and deflections and compared to those captured at midspan. Finally, it highlighted that the midspan of the beam cannot be a valid reference to obtain the true maximum deflections and flexural moments of the base beam.

Keywords: Moving mass, Euler-Bernoulli beam, dynamic response, normalized maximum dynamic response

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