The Study of Vibrations: Mathematical Modelling and Classifications

The matter is made up of particles, firmly assembled, as in the solids, or rarefied, as in the gases. When a force acts on a particle it moves determining different physical phenomena depending on the different characteristics of that particle and the surrounding ones.-This model represents the action of a blast or a mechanical pulse, just one hit and the system can manage the supplied energy by damping and distributing it. Each system has a specific behavior, mainly depending on the frequency of the stressing force; if the system has a frequency of resonance whose value is close to the frequency of the stressing force, energy is stored in the system, movements of the particles become larger and, at the end of the energy supply, the system continues to oscillate, giving back the stored energy, implying that the longer the oscillation the lower is the damping. The vibration of a physical system can propagate the movement through a vibrational wave, generated by the application of external forces generating internal stress, strain and reaction, a disturbance that travels through a medium from one place to another like a wave. When the vibration is forced by a mechanical system, the stimulus can be applied in order to generate a different kind of vibration. In order to generate a vibration, it is necessary to apply an external force: however, the response of a mechanical system to an external force can vary not only depending on the nature of the stimulus, but also according to the composition of the system itself. The mathematical model of a vibration system may take the form of acoustic waves.

Keywords: Mathematical modelling, Matter, Vibrations, Ways of propagation.