In order to simplify the resolution of the equation of motion, structural damping is generally supposed to be proportional. Indeed, this coarse and unjustified hypothesis leads to uncoupled equations of motion in the modal basis. The aerodynamic and concentrated dampings (dash-pots) are accurately characterized by mathematical laws. These are such that the equations of motion are no longer uncoupled in the modal basis. After presenting the usual ways to solve coupled system of equations, the paper focuses on a method based on Taylor series expansions which allows to partially account for the coupling. After developing the equations related to this method, some examples of application are provided.
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