Modes of vibration, natural frequency

  1. Hi.. I have a question about natural fvibration.
    Every object has natural frequency and modes of vibration.
    Let us consider a simple cantilever beam for our discussion.
    and Lets say its first 4 modes of vibration are at 3, 6, 10 and 20 kHz respectively.
    (I made up these frequency values)
    Now, my question is.. if we pluck the cantilever and let it free vibrate by its own..
    "Why will it ever vibrate at second or third modes?"
    My feeling is that it always vibrates only at first mode.
    Is it not right?
    It can go to higher modes in forced vibration but I do not see any reason
    why it goes for higher modes in a free vibration.

    Please talk about this.

  2. jcsd
  3. FredGarvin

    FredGarvin 5,084
    Science Advisor

    When you pluck something like that you excite all modes at once. They are all there. If you were to do some modal analysis and instrument the beam in enough locations, you would be able to see all modes at once. Another way we do it is when we pluck aerodynamic blades. We hold a microphone up very close to the blade and pluck it. When this happens the mic pics up all of the vibrations. We send that time signal through an FFT and we see the first 9 or so modes that are usually of a concern. The issue as to whether you excite a mode is really if you impart enough energy into a system to actually excite it.

    I would suggest doing some research on modal analysis.
  4. Dear Fred
    Thank you for your reply.
    So..It means when we pluck and leave a beam, its vibrates at its modes of natural frequency.. did i get it right? If we pluck a beam having 1, 3, and 8 kHz as its first
    three modes, in its FFT, we get three peaks at those frequencies..provided we sense
    if properly... is it right?

  5. FredGarvin

    FredGarvin 5,084
    Science Advisor

    That is pretty much correct.
  6. by definition the natrual frequencies are the modes it will oscillate at on its own accord.

    Oscillation at any other frequency will have to be induced into the system via an input forcing function.
  7. hi there...
    If I force a vibration into an object, and then remove the forcing conditions, will the object still keep vibrating??
    The bob experiment given on this link... It says that the red bob forces the metal bar to vibrate at its natural frequency, which vibrates the other red bob. But, as the other bobs do not share the same natural frequency, they won't vibrate.
    Won't they be forced into vibration by the metal bar??
    (Last post said that oscillations other than the natural frequency can be induced into the system...)
  9. wbf

    wbf 2

    It is important to mention that the free vibration response of a structure depends upon what frequencies you are exciting by the spectrum of your input - i.e the magnitude and shape of the force you apply to the bar it to set it vibrating.

    If you could give the bar an impact with a pure impulse function (a strike with infinitely small contact time), the strike would excite all frequencies (up to infinity). As the FFT of an impulse is a flat line covering all frequencies up to infinity.

    In reality, your flick or push may be closer to a half-sine wave function. If you know Fourier analysis, you will see that the FFT of a half-sign wave function is a wave type function that dies off at a certain point. The half-sine wave will excite frequencies in a certain range given by the width of the pulse (in time). The smaller the width of the half-sine wave, the higher the frequency ranges will be excited. The larger the width, the lower the frequencies that will be excited.

    When you do impact testing with a hammer on a structure, you can use different materials for the tips on the hammer to excite different frequency ranges. The softer the tip, the lower the frequencies that will be excited and vice versa for higher frequencies.
  10. modes of vibration vs. flexural modes

    I am working on building and running a test setup based on a very old spec. It is my first time flying solo so to speak. I need some advice. The spec reads "The free bar shall be excited at each of the first seven lengthwise flexural modes of the bar."

    Does this mean:

    a) as in measurements at the first 7 node points along the physical length?


    b) the first seven modal frequencies measured from the same location?

    This will be to find the percent critical damping. I will use an electrodynamic exciter with a stinger for mechanical attachment.

    any ideas?
  11. FredGarvin

    FredGarvin 5,084
    Science Advisor

    B is the correct one.
  12. wbf

    wbf 2

    Yep. I agree with Fred Garvin. I say B is the correct one. The spec means to use the exciter to shake the bar at each of the first 7 frequencies.

    With the exciter you should be able to dial in the amplitude and frequency of oscillation, so you can excite one frequency at a time (in theory).
  13. It would certainly make the most sense. I agree. Thanks for the input!
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