Reduction method applied to viscoelastically damped finite element models

International audienceWe propose in this paper to combine the GHM (Golla-Hughes-Mc Tavish) method with model reduction technique, especially direct condensation methods to resolve the problem of increased model order of viscoelastically structures. In fact, modeling structures using the GHM method leads to global systems of equation of motion whose numbers of degrees-offreedom largely exceeds the order of the associated undamped system. As result, the numerical resolution of such equations can require prohibitive computational (CPU) time. So, to overcome this problem, both Static and Dynamic methods are used to reduce the order of finite elements matrices while preserving its capability to represent the dynamic behavior of viscoelastically damped structures. This paper intends to compare these two methods in direct reduction. Numerical example applied to cantilever beam structure is presented. This example will highlight the domain of validity of the studied methods. Results obtained from these two reduction methods are compared with the full model in order to illustrate its performances and its practical interest in the dynamic analysis of viscoelastically damped structures