Spatially coupled vibrations of a suspension bridge under random highway traffic

Abstract

SUMMARYThe problem of spatial dynamic response of a suspension bridge to the passage of trains of concentrated forces with random values is considered. The arrival of forces at the bridge is assumed to constitute a Poisson process of events. Such an excitation process is an appropriate model of vehicular traffic loads acting on the bridge. The bridge is idealized by a single-span thin-walled beam underslung to two cables. The response of the bridge in the space-time domain is described by a coupled system of non-linear, integro-differential equations. The dynamic influence functions of vertical 2nd horizontal deflections at each cross-section point are obtained for the linear case. Cumulants and probability density functions of response are determined. Numerical methods have been used to develop a computer-oriented algorithm aimed at the numerical solution of the problem. As examples, numerical results for a particular bridge with some practical load cases are presented and illustrated by graphs.

Application of Volterra Integral Equations in Dynamics of Multispan Uniform Continuous Beams Subjected to a Moving Load

“…Function ( ) is used to describe aperiodic vibrations of the beam and does not satisfy the initial conditions (10). Function ( ) is used to describe free vibrations and results from the homogenous equation̈( ) + 2 = 0 and together with function ( ) satisfies zero initial conditions of motion.…”

“…while constants and result from the zero initial conditions (10) After solving (8) taking into account the initial conditions (10) the response of the beam has the form…”

“…The function ( , ) in expression (16) describes the aperiodic vibrations and satisfies the nonhomogeneous differential equation 4. This function does not satisfy the initial conditions of motion (10). The function ( , ) is the free vibrations of the beam which satisfy the homogeneous differential equation (4) ( = 0) and together with the aperiodic function satisfy the initial conditions of motion (10).…”

“…Original solutions in a closed form for the aperiodic vibration of the finite, simply supported Euler-Bernoulli beam, Timoshenko beam, and a sandwich beam are given in the papers [5][6][7]. Also more complex systems like a double-string, a doublebeam, or a suspension bridge have been considered as singlespan girders [8][9][10][11][12]. An important and interesting problem is the vibrations of a multispan beam caused by a moving load.…”

Vibration of a suspension bridge installed with a water pipeline and subjected to moving trains

“…Early works on this subject, including those by Bleich et al [1], Rocard [2], Pugsley [3], and Abdel-Ghaffar [4], have laid the foundation for further studies on various dynamic problems of suspension bridges. Partly stimulated by the completion of numerous suspension bridges in the past two decades worldwide, the dynamic behavior of suspension bridges under moving loads has also attracted the attention of numerous researchers [5][6][7][8][9][10][11][12]. In all these studies, an important conclusion is that significant amplification may be induced by the moving loads on the cable forces for short-span suspension bridges.…”