Modal, Static, Harmonic, Transient-Dynamic and Random Vibration Analyses of a Two Degree of Freedom System by Matlab and Ansys

Abstract

Static, harmonic, transient-dynamic and random vibration analyses are widely used to design structures. Commercial finite element (FE) programs such as ANSYS are used to analyze structures with complex geometries. However, FE programs can produce erroneous results if the user makes even minor mistakes. Thus, it is important to understand the basic theory of FE solutions. The purpose of this work is to give the introductory theory of FE solutions by considering a two degree of mass-spring system. The MatLAB programs based on the analytical solutions are given. The MatLAB results are compared with the FE results by ANSYS. The system is modeled in SolidWorks and imported to ANSYS. Modal, static, harmonic frequency response, impulse response, and random vibration responses are considered. Modal and static analyses for unconstrained systems are also considered. The results obtained by MatLAB and ANSYS are in good agreement. The results of this study can be used by the users of other simulation programs for comparison. © The Author(s) 2025.