ECCOMAS Congress 2016 VII European Congress on Computational Methods in Applied Sciences and Engineering M. Papadrakakis, V. Papadopoulos, G. Stefanou, V. Plevris (eds.) Crete Island, Greece, 5–10 June 2016 FINITE BEAM ELEMENT WITH PIEZOELECTRIC LAYERS AND FUNCTIONALLY GRADED MATERIAL OF CORE Vladim´ ır Kutiˇ s 1 , Just´ ın Mur´ ın 1 , Juraj Paulech 1 , Juraj Hrabovsk´ y 1 , Roman Gogola 1 and Jakub Jakubec 1 1 Department of Applied Mechanics and Mechatronics Institute of Automotive Mechatronics Faculty of Electrical Engineering and Information Technology Slovak University of Technology in Bratislava Ilkoviˇ cova 3, 812 19 Bratislava, Slovak Republic e-mail: vladimir.kutis@stuba.sk, justin.murin@stuba.sk, juraj.paulech@stuba.sk, juraj.hrabovsky@stuba.sk, roman.gogola@stuba.sk, jakub.jakubec@stuba.sk Keywords: Piezoelectric Material, FGM, FEM, Beam Element, Transient Analysis Abstract. New smart materials have been developed in material science, that are suitable for mechatronic applications. Modern mechatronic systems are focusing on minimizing size, active control and low energy consumption. All this attributes can be incorporated into term Micro Electro Mechanical Systems (MEMS). To improve performance of MEMS system, new materials and technologies are developed - one of them, which found broad application usage is Func- tionally graded material (FGM). MEMS application usually contains multilayer structure and in some application class MEMS systems contain piezoelectric layers. Piezoelectric structures offer facilities to make motions. Piezoelectric layers can be also used to damp vibrations as an active damping or as an active sensor. For better understanding these multiphysical problems new mathematical models are developed. The paper deals with finite beam element with piezoelectric layers and functionally graded ma- terial of core. In the paper homogenization of FGM material properties and homogenization of core and piezoelectric layers is presented. In the process of homogenization direct integra- tion method and multilayer method is used. There is also presented the derivation of individual submatrices of local stiffness and mass matrix, where concept of transfer constants is used. Functionality of new FGM finite beam with piezoelectric layers is presented by numerical ex- periments. 4863