Matrix computations (3rd ed.)
The Scaling and Squaring Method for the Matrix Exponential Revisited
SIAM Journal on Matrix Analysis and Applications
Assessment and improvement of precise time step integration method
Computers and Structures
Enhancement factors for the vertical response of footbridges subjected to stochastic crowd loading
Computers and Structures
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This paper presents a computationally efficient methodology for determining footbridge vibration response when subject to pedestrian excitation suitable for use in a Monte Carlo framework. A general modal precise integration method is developed for moving force problems. A closed-form solution for the transition matrix for the important case of a simply-supported beam subject to harmonic moving loads is given. The proposed method is efficient and accurately estimates important statistics of response in pedestrian excitation problems. This method should therefore find value in assessing new or existing footbridges when subject to random pedestrian excitation.