Vibration of damped uniform beams with general end conditions under moving loads. (1st November 2016) - Svedholm, C.
Highlights: Analytical solution for a non-proportionally damped beam under moving loads. The solution is useful for studying various types of damping mechanisms in bridges. Examples are included to provide insight into the problem of damped systems. Interesting results are presented for closely spaced modes. Abstract: In this paper, an analytical solution for evaluating the dynamic behaviour of a non-proportionally damped Bernoulli–Euler beam under a moving load is derived. The novelty of this paper, when compared with other publications along this line of work is that general boundary conditions are assumed throughout the derivation. Proper orthogonality conditions are then derived and a closed form solution for the dynamical response for a given eigenmode is developed. Based on this, the dynamical response of the system to any load can be determined by mode superposition. The proposed method is particularly useful for studying various types of damping mechanisms in bridges, such as soil–structure interaction, external dampers, and material damping. Several numerical examples are presented to validate the proposed method and provide insight into the problem of non-proportionally damped systems. The numerical examples also allow for some interesting observations concerning the behaviour of modal damping for closely spaced modes (with respect to undamped natural frequencies).