Mathematical modelling of structures using model order reduction technique

Abstract

Today’s world is a world of simulation. Now a days, every product is first designed in virtual domain and then tested for actual implementation. To be able to perform such accurate virtual domain analysis, an accurate mathematical model is needed to be designed in first place. Specifically, in the field of dynamic analysis, so as to continuously monitor the system, the requirement a high-fidelity simulation models in all industries is rising rapidly and this has now become an important part of modern simulation strategies. FEA simulation software’s nowadays could provide very accurate results but they cannot be used directly for dynamic simulations where the environment is continuously changing (input forces, random vibrations etc.). Therefore, this paper deals with design of a mathematical model of a beam to overcome the above stated issue. The technique so used is Model Order Reduction. This method develops an efficient reduced model by reducing the degrees of freedom and also preserving a characteristic behavior of the system. The methodology deals with extracting the mass, and stiffness matrices from FEA simulation software, reducing their size (order), building a second order system using reduced sizes of mass and stiffness, analyzing mode shapes vectors and nodes for input force applications, and generating a state space model of the system.