Vibration Analysis: Validation of the Mathematical Model and the Physical Simulink Multibody Model

Özet

Partial differential equations (PDEs), matrices, eigenvalues, and eigenvectors are foundational concepts in mathematics and play a critical role in various scientific and engineering applications. PDEs describe the relationship between functions of multiple variables and their partial derivatives, enabling the modeling of complex phenomena such as heat transfer, fluid dynamics, and electromagnetic fields. Eigenvalues and eigenvectors, derived from matrix theory, are essential in understanding the behavior of linear transformations and play a pivotal role in solving systems of differential equations, stability analysis, and in applications like quantum mechanics, structural engineering, and machine learning. Understanding these concepts provides a deeper insight into the structure of systems, allowing for more accurate predictions and optimizations in real-world problems. This study investigates the important role of partial differential equations (PDEs) and matrices in mechanical vibration systems. It presents the modeling of a two-degree-of-freedom system, which includes both rotational and translational motion. The vibration analysis for the given system is conducted using PDEs, matrices, eigenvalues, and eigenvectors. The same analysis, under the same conditions, is then demonstrated through a multibody physical model and non-linear motion equations, with computations performed in Simulink/MATLAB. As a result, the three methods are validated to verify the analysis.