Natural frequencies and mode shapes

  1. 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!
  2. jcsd
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