Solution of the free vibration equation of a multi span bridge deck by local estimation method

The study of the dynamic behavior of the roadway bridges solicited by the mobile vehicles’ passage is a topicality subject, which interests many researchers in different fields. In this work, we present a roadway bridge modeling by the equation of motion of a multi span orthotropic thin plate. We propose to solve the free vibration equation by separation of variables leading to an equation of motion with varying coefficients by the longitudinal position, estimating the coefficients at anti nodes of the mode shapes of the beam. The proposed method allows us to obtain good approximations of natural frequencies and mode shapes of the bridge. This new method is very efficient compared to the previous methods, because it is analytical and avoids carrying out several integrations as in the case in the Rayleigh–Ritz method. The results obtained by the suggested method are very close to those obtained numerically by ANSYS software; the variation does not exceed 2.5%. The obtained results show a good agreement to the previously published results mainly for the bending modes, whereas the difference becomes important for the mode shapes of the second order. The difference can be explained by the consideration, in previous works, the beam boundary conditions whereas in our work, plate and beam boundary conditions are used.

► Solve the motion equation only once using a simple criterion for the optimal position.
► The optimal position coincides with the mode shape maximum amplitude of the beam.
► This approach minimizes drastically the computing time, produces satisfactory results.
► Good concordance results comparable with those of the literature, ANSYS simulation.
► The proposed method can be easily integrated in a calculated structure software.