Dynamic substructuring for visco-elastic materials using a POD-based model reduction method: application to laminated panels

Dynamic substructuring is now a well established and powerful tool for engineers used to analyze the dynamic response of mechanical systems. The technique is particularly favored for the simulation of mechanical vibrations allowing different aspects to be studied. It consists in splitting the global structure into several substructures from which reduced models are built. In Finite Element software, these reduced models, also called superelements, are generally built using the concept of Component Mode Synthesis. Difficulties arise when structures made of frequency-dependent materials are considered since classical modal reduction algorithms are inapplicable as they are because of the frequency-dependence of the stiffness matrix. Based on the Balanced Truncation approach, a novel methodology for the construction of a superelement for the dynamic analysis of elastic structures made with viscoelastic materials is presented. The methodology takes advantage of the Golla-Hughes-McTavish rheological model (GHM) before reducing the system via the Balanced Proper Orthogonal Decomposition (BPOD). The coupling of the superelement with a host structure is achieved via the use of Lagrange multipliers. The reduced system takes the form of a constant matrix of very small size compared to the original FE model. The method is applied to laminated panels such as an automobile windscreen.