Dynamics of damped rotating solids of revolution through an Eulerian modal approach

This article presents a technique for modelling the dynamic response of rotating flexible solids with internal modal damping. The method is applicable to solids with geometry of revolution that rotate around their main axis at constant spinning velocity. The model makes use of an Eulerian modal coordinate system which adopts the vibration modes in a non-rotating frame as basis functions. Due to the coordinate system, the technique is particularly suitable for studying the dynamic interaction between rotating solids and non-rotating structures and permits to obtain Frequency Response Functions. The current investigation presents the development of the proposed technique from a previous Lagrangian model, and consequently the mathematical relationships between the two coordinate sets are found. The approach has been adopted to study the dynamics of a simply supported cylinder including damping in order to obtain the receptance function and the modal properties of the rotating solid.

► We model the dynamics of flexible solids of revolution with internal damping. ► We give formulae relating Lagrangian and Eulerian coordinates based daming ratios. ► Using Eulerian coordinates facilitates response analysis in non-rotating coordinates.