High Efficiency Method For Bridges Subjected To Moving Loads

Newmark integration method has hitherto been in common use to solve problems on dynamic analysis of bridges subjected to moving loads. However, it assumes that the magnitude and position of the load are both invariant during each time step and so jump suddenly at the interfaces between time steps. Thus the continuously varying magnitudes and positions of the loads are replaced by a series of constant load impulses acting at a succession of fixed points. This approximation results in significant errors even for very small time step sizes, particularly for rapidly varying loads. In the present paper the precise integration method (PIM) combined with the finite element technique is extended to allow the magnitude and position of the moving loads to vary within each time step, by developing and investigating three different precise integration formats. Thus the continuous movement of the loads is well simulated and there are no jumps at the interfaces between time steps. Comparing the efficiency and precision with those obtained by using the Newmark integration method, the results show that even when a time step contains several periods of the excitation, the proposed extended PIM still gives very accurate results.On the basis of the above methods, pseudo excitation method (PEM) is used to solve the problems on the response analysis of bridges subjected to moving random loads. Assume the mean value of the loads be constant, so the excitation can be regarded as a uniformly modulated evolutionary random process. Then the pseudo harmonic loads attained from PEM can be used to deduct the power spectral density functions and variances (standard deviations) of interested bridge responses. It is shown from numerical comparison that PEM is much more efficient than the conventional methods for resolving random response of bridges.