Dynamics: Resonance

To see a resonant response, it requires an input device that can generate either harmonic base motion, such as a shaking table, or harmonic load, such as using a vibrator, together with a simple structure that has a natural frequency within the frequency range of the input.

Dynamic response of a SDOF system subject to harmonic support movements

This demonstration shows the observations obtained from Figs. 16-3 and 16-8, i.e. the relationship between the response of a SDOF system and the ratio of the frequency of input to the natural frequency of the system.

Fig. 16-9: The model of a SDOF system

An elastic string and a mass can form a simple SDOF system as shown in Fig. 16-9. Hold the end of the string and move it up and down harmonically to simulate the harmonic support movement of the SDOF system. This corresponds to the model shown in Fig. 16-6. The movement of the mass can be described using Eq. 16-24, and the ratio of the maximum movement of the mass to that of the hand is shown in Fig. 16-8.

The dynamic phenomena shown in Fig. 16-8 can be demonstrated qualitatively as follows:

• The person holding the string first moves his/her hand slowly up-and-down, creating a situation where the frequency of the support (hand) movement is much smaller than the natural frequency of the SDOF system. It will be observed that the amplitude of movement of the mass is almost the same as those of the support (hand), as indicated by Fig. 16-8 when the frequency ratio is less than 0.25.
• When the hand moves up-and-down quickly, it creates a situation that the frequency of the hand movement is larger than the natural frequency of the system. It can be seen that the hand movements are much larger than the movements of the mass, as indicated in Fig. 16-8 when the frequency ratio is larger than 2.0.
• Finally, when the hand moves up-and-down at a frequency close to the natural frequency of the system, a situation is created in which resonance develops. It is observed that the movements of the mass are much larger than the hand movements, as indicated in Fig. 16-8 when the frequency ratio is near to unity.