Modeling and response analysis of dynamic systems by using ANSYS© and MATLAB©

Abstract

In the last decade, many advances and changes have been seen in engineering theory and applications. The modern trend is to combine modeling, theoretical analysis and computer simulation. The conventional techniques of mathematical modeling of real life complicated structural systems for vibration analysis are tedious and time consuming. The finite element (FE) method is becoming popular because of its simplicity and feasibility of using for real life applications. In the present study, extraction of the system model from its FE model by using commercially available softwares such as ANSYS© and MATLAB© is demonstrated. A two-degree-of-freedom spring-mass-damper system is considered here. Its state space mathematical model in principal coordinate system is obtained in MATLAB© from the modal analysis results of its FE model done in ANSYS©. For checking the validity of model, transfer function and state space model in physical coordinates of the same system are derived mathematically by assuming proportional damping. Frequency responses of all the system models are compared and found to be in good agreement. To demonstrate the application of this study, system model of a cantilever beam is also extracted in MATLAB© from the result of modal analysis of its FE model in ANSYS© and its frequency response is plotted. Response of cantilever beam to unit impulse input is also obtained in both ANSYS© and MATLAB© and compared for validating the model. This study will definitely help in simplifying the vibration analysis of real life systems.