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assume we have a multi-dof system and a force is applied with same frequency as one of the natural frequencies. will this system be resonant in any circumstances? (system is undamped).

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    $\begingroup$ A common mistake people make here is they assume everyone knows every acronym. It is always helpful to spell out the full term before using an acronym. What is "multi-dof"? $\endgroup$
    – Fred
    Apr 27 '17 at 8:43
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That resonance is exactly why most systems are designed to avoid vibrating at the natural frequency - there are many examples of the consequences - see the (millenium I think...) bridge in London people walked, bridge moved, people started to walk in step, bridge moved even more...

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  • $\begingroup$ will this happen always? my teacher said there is one exception but didn't say what is that. $\endgroup$
    – SaDeGH_F
    Apr 27 '17 at 7:15
  • $\begingroup$ Tuning forks - musical instruments? $\endgroup$
    – Solar Mike
    Apr 27 '17 at 7:23
  • $\begingroup$ @SaDeGH_F maybe your teacher is referring to the position of the actuator, for example applying a periodic force to a beam at a node of the standing wave corresponding to that frequency should hardly excite the system. $\endgroup$
    – fibonatic
    Apr 28 '17 at 10:32
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A Multi-DoF (system with multiple degrees of freedom) can be linear or nonlinear.

For linear systems in most cases, the system will enter resonance. The application of so-called mass dampers can be used to avoid the resonance peak. The theoretical advantage of linear systems is that we know that there is no dependence of amplitude and frequency from the external excitement for the resonance frequencies and modes of resonance of the system.

For the nonlinear system, we observe that the resonance frequencies are depending on the amplitude and frequency of the external oscillations. In general, the term mode of resonance is not applicable for nonlinear systems. Additionally, there are a lot of effects that make vibrations of nonlinear systems very difficult to describe.

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