Abstract:

Linear single-degree-of-freedom systems are particularly important in the study of vibrations for several reasons. First, despite their simplicity, they are able to model the behavior of relatively complicated components or mechanical systems, used in technical applications. Second, due to their simplicity, the equations of motions generally have closed form solutions; this makes them easy to use in numerical applications. Third, by the generalization of their properties, multi-degree-of-freedom systems can be understood more easily.

The paper presents an educational computer program, developed by the authors, aimed for the graphical animated simulation of the vibrations of single-degree-of-freedom systems.

The program utilizes a simple mechanical model, consisting of a rigid body in translation motion, connected to the fixed element by a spring and, in certain cases, by a damper. This model is used for the study of all usual types of vibrations of such a system: free undamped vibrations; free damped vibrations; forced undamped vibrations produced by the action of a harmonic perturbation force (outside the resonance regime and at resonance, respectively); forced damped vibrations produced by the action of a harmonic perturbation force. The program computes vibration-specific quantities: circular eigenfrequency, eigenperiod, eigenfrequency, damping ratio, ration between perturbation circular frequency and circular eigenfrequency. The motion of the system is displayed by an animated representation.

The paper is structured in three parts, of which the first part briefly presents the analytical basis, the second part describes the program, including its user interface and functionality, while the third part proposes a method for integrating the program in practical sessions of the course of vibrations taught in engineering faculties.

Keywords:

Damped vibrations, free vibrations, resonance, e-learning.