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Using modal damping for full model transient analysis. Application to pantograph/catenary vibration

Experimentally, modal damping is known to allow a relatively accurate representation of damping for wide frequency ranges. For transient simulation of full finite element models, viscous damping is very often the only formulation that is associated with an acceptable computation time. In the absence of a proper material damping model, it is common to assume Rayleigh damping, where the viscous matrix is a linear combination of the mass and stiffness, or piece-wise Rayleigh damping. This representation very often results in modal damping ratios that do not correspond to the physical reality that can be tested. One thus introduces an implicit representation of the viscous matrix that allows transient time simulation with minor time penalty, while using a much more appropriate damping representation. Modal amplitudes are also considered to postprocess time simulations and analyze damping levels. When studying vibrations induced by the passage of pantographs under a catenary, the high modal density of catenaries and the load moving over a large part of the model is a strong motivation to use full model transient analysis. Modal damping is shown to be a practical tool to analyze the properties of this complex system.