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Model Order Reduction (MOR) methods such as Component Mode Synthesis (CMS) have been used in order to simulate large linear dynamic systems for many years and have reached a considerable level of saturation. These reduction methods have many advantages such as minimizing computational costs but also have restrictions. One of their disadvantages is that material damping characteristics can only be defined in form of Rayleigh damping. Another disadvantage is that the reduced order model can only represent one state of the structure determined in the generation process of the reduced matrices. In this paper we present a way to consider material damping in reduced matrices that contain one or more materials having different damping characteristics without the disadvantages of using Rayleigh damping.