Vibration of Parabolic Tied-arch Beams Due To Moving Loads

This paper intends to study the train-induced vibration of a parabolic tied-arch bridge using an analytical approach. The train loads over the bridge are regarded as a sequence of equidistant moving loads with identical weights. The tied-arch bridge considered is modeled as the combination of a parabolic flat-rise arch with two-hinged supports and a simple beam suspended by densely distributed vertical cables connected to the arch rib. Using the normal coordinate transformation method, the coupled equations of motion of the arch rib and suspended beam are converted into a set of uncoupled equations. Then, one can derive closed form solutions for the response of the tied-arch beam to successive moving loads, by which the resonant conditions of higher modes of the suspended beam can be identified. According to the present study, the critical position for the maximum acceleration on the suspended beam depends upon the vibration shape that has been excited. Moreover, the numerical results indicate that the lower the rise of the arch rib, the larger the acceleration response of the main beam suspended by the arch.