Natural frequencies and mode shapes

[reast_reast]

Hi people, we were doing an experiment in lab where we excite a plate clamped at the circumference at various frequencies to detect natural frequencies. My questions are:

1. Sometimes at certain frequencies, we were observing multiple mode-shapes (an overlap of two mode shapes, to be exact). What is the reason? It probably has to do something with the imperfection in our set-up. Does anyone have a more definitive answer?

2. The first theoretical natural frequency was 160 Hz. However, in reality, we observed the same mode shape at 80 Hz and 160 Hz. What may be a reason?

3. Why amplitude of vibration at natural frequencies decreases with increasing natural frequencies? i.e. first mode shape (and lowest natural frequency) has the highest amplitude, and the later shapes have lower amplitude. I was thinking frequency is proportional to the square root of the elastic modulus. But it's not the complete answer (TA told me). Does it have anything to do with energy and power?

Thank you a lot for your help!

 

[NateD]

1. The overlapping of two mode shapes could be due to the imperfection in your set-up, or it could also be due to resonance phenomena. Resonance occurs when an object is being excited with a frequency that matches its natural frequency, which causes the object to vibrate at a higher amplitude. In this case, two different frequencies could be resonating with the plate, causing the overlap of mode shapes. 2. The reason why you are observing the same mode shape at 80 Hz and 160 Hz could be because of the damping of the system. Damping is the dissipation of energy from the system, which can cause the resonant frequency to shift slightly. In other words, the damping of the system is causing the resonant frequency to shift, thus producing the same mode shape at both 80 Hz and 160 Hz. 3. The decrease in amplitude of vibration with increasing natural frequencies is due to energy dissipation. As the frequency of the plate increases, more energy is dissipated and the amplitude of the vibration decreases. This is why the first mode shape (and lowest natural frequency) has the highest amplitude, and the later shapes have lower amplitude.