Multi-harmonic Vibration Mitigation Through Exploitation of Structural Instability

Anna Allen Author

08/04/2020 Added

30 Plays

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This project tests a Bunyan-Tawfick spring's ability to mitigate vibrations at multiple frequencies.

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[00:00:00.000]Hello my name is Anna Allen, I am an
[00:00:02.769]undergraduate mechanical engineering
[00:00:04.806]major at the UNL, and first I would
[00:00:06.841]like to thank you for taking the time
[00:00:08.883]out of your day to watch my
[00:00:10.328]presentation. Today I will be presenting
[00:00:12.304]about my summer research project Multi-
[00:00:14.208]harmonic vibration mitigation through
[00:00:16.478]Exploitation of Structural Instability,
[00:00:18.588]and with that I would like to move into a
[00:00:20.988]brief discussion of the focus of this
[00:00:23.136]research.
[00:00:24.905]This project focuses on vibration
[00:00:28.905]mitigation – reducing vibration – on our
[00:00:32.949]proposed system, which is an airplane wing
[00:00:35.180]Reducing vibration in mechanical systems
[00:00:37.599]is vital for the safe operation of many
[00:00:40.627]different systems, not just airplanes. A
[00:00:44.367]promising approach to vibration mitigation
[00:00:46.517]is using what are called “Nonlinear Energy
[00:00:48.907]Sinks” which henceforth will be referred
[00:00:51.347]to as NESs. An NES is a strongly nonlinear
[00:00:55.347], broadband vibration absorber that
[00:00:57.732]changes frequency with respect to the
[00:00:59.733]amplitude of the response. Specifically,
[00:01:02.639]they are used to mitigate vibrations at a
[00:01:04.679]wide range of frequencies; however, they
[00:01:07.121]only work if they have a low-amplitude
[00:01:09.291]frequency less than the frequency they are
[00:01:11.841]trying to mitigate. The figures on the
[00:01:14.931]left show an example of an NES being
[00:01:17.669]used as a vibration absorber for a
[00:01:20.123]harmonic oscillator. The NES here is
[00:01:23.748]represented by the mass MNES and has been
[00:01:27.098]installed on top of this harmonic
[00:01:31.098]oscillator. The mass of the Linear
[00:01:33.895]oscillator, or the LO, is represented by
[00:01:36.593]MLO. While D1 & D2 represent the damping
[00:01:43.241]for the system. On the right, it can be
[00:01:47.531]seen how the NES can help dissipate energy
[00:01:50.501]These are plots of the displacement
[00:01:52.599]response with the harmonic oscillator
[00:01:55.383]alone in black and the harmonic oscillator
[00:01:57.824]with an NES attached in red. The plot on
[00:02:01.824]the top is for a low linear coupling
[00:02:04.284]stiffness and the NES does its job, it can
[00:02:07.234]be seen that energy is being dissipated
[00:02:09.534]through the reduction of the oscillations.
[00:02:19.356]The plot on the bottom, however has a high
[00:02:25.823]linear coupling stiffness and thus the NES
[00:02:28.433]doesn’t absorb as much energy. Mitigating
[00:02:33.357]low-frequency vibrations with an NES is
[00:02:35.990]difficult because it is hard to create an
[00:02:38.201]NES with a low linear stiffness.
[00:02:42.201]To solve this problem the project proposes
[00:02:46.010]taking advantage of structural instability
[00:02:49.058]by using a Bunyan-Tawfick, or BT, spring
[00:02:51.994]with the NES. In this Figure an image of
[00:02:58.553]the actual spring can be seen going throug
[00:03:01.212]a loading cycle. This spring creates a
[00:03:03.734]unique force vs. displacement curve in the
[00:03:06.854]beginning it behaves linearly, then the
[00:03:10.514]force plateaus because the spring begins
[00:03:12.801]to buckle and then after a point it begins
[00:03:15.738]to stiffen. The equation shown is used to
[00:03:19.738]model this force. Using the equation, we
[00:03:23.296]performed a curve fitting procedure to
[00:03:26.576]identify the parameters. As you can see in
[00:03:29.291]this figure, the black line represents the
[00:03:31.855]experimental values, and the red line
[00:03:33.993]represents the values from the equation.
[00:03:35.984]This plot was made in a program called
[00:03:39.054]matlab, and a code was written to find the
[00:03:41.805]values for the equation to get the red lin
[00:03:45.005]as close to the black line as possible.
[00:03:47.851]These values are displayed here on the
[00:03:52.881]slide as well. The unique force-
[00:03:57.611]displacement curve of the BTspring will
[00:04:00.252]allow the NES to decrease and mitigate
[00:04:02.462]vibrations at low frequencies.
[00:04:09.762]Once again we have model of the LO-NES
[00:04:13.762]system and the corresponding parameters
[00:04:17.762]for the BT spring system. These plots show
[00:04:20.899]how a different initial velocity affects
[00:04:22.899]the results of a spring. The plots in blue
[00:04:25.767]are called wavelet transforms and wavelet
[00:04:28.384]transforms provide a time-frequency
[00:04:30.851]representation of the content contained in
[00:04:33.562]the signal. Now you can see here on the
[00:04:37.322]left the displacement response and wavelet
[00:04:40.394]transform for a low energy with an initial
[00:04:42.987]velocity of 0.05. The right displays the
[00:04:47.547]same, but for a higher energy with an
[00:04:50.059]initial velocity of 0.5. You can see the
[00:04:53.591]frequency of the NES on the left is higher
[00:04:57.162]but when we increase the energy the
[00:04:59.638]frequency decreases.The figure on the left
[00:05:05.828]in this slide displays energy dissipated
[00:05:09.253]by the oscillator versus the initial
[00:05:12.057]velocity. You can see this circle indicate
[00:05:16.675]where the initial velocity is low and the
[00:05:19.837]NES dominates when it comes to energy
[00:05:22.685]dissipation. Now, this figure on the right
[00:05:36.763]shows the displacement and wavelets of the
[00:05:40.763]LO with the NES compared to the
[00:05:43.763]displacement of the LO alone at this
[00:05:46.980]initial velocity, which is near 0.1. With
[00:05:58.188]a wavelet plot the darker a portion is the
[00:06:02.588]more that the signal was present at that
[00:06:05.314]time, using this knowledge we can see that
[00:06:07.842]the majority of the signal for the LO-NES
[00:06:11.223]happened in a very short timespan compared
[00:06:16.046]to the harmonic oscillator case. This can
[00:06:31.688]also be seen in the displacement plot
[00:06:37.835]where the amplitude is decreased. This
[00:06:47.945]slide displays more results. The figure
[00:06:50.094]on the left displays the energy-dissipated
[00:06:52.304]versus initial energy once again, and this
[00:06:55.256]time the circle indicates the behavior
[00:06:57.796]near the middle of the plot where the NES
[00:06:59.835]dominates again. The figure on the right
[00:07:02.884]has the displacement of the LO with the
[00:07:05.576]NES and harmonic oscillator. In this
[00:07:08.410]figure we can see again that the
[00:07:10.393]oscillations in the displacement plot are
[00:07:12.864]dissipated quickly and in the wavelet the
[00:07:15.874]response of the LO-NES is much shorter.
[00:07:19.682]These results slides show how extremely
[00:07:23.319]effective the BT spring has been at energy
[00:07:25.591]dissipation at different excitation levels
[00:07:32.601]We investigated the behavior of the bunyan
[00:07:35.801]-tawfick spring for use in a nonlinear
[00:07:38.801]energy sink. We found that even though it
[00:07:41.861]starts with a frequency higher than that
[00:07:43.895]which we wish to dissipate, it is still
[00:07:47.276]able to mitigate energy. We also found
[00:07:50.235]that the bunyantawfick spring is affective
[00:07:52.435]across a wide range of initial velocities.
[00:07:54.695]Future research is going to focus on an
[00:07:56.910]experimental implementation of the BT in
[00:08:00.731]an existing LO-NES system and from there
[00:08:03.766]we want to investigate
[00:08:05.273]applying this to a model airplane.

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Multi-harmonic Vibration Mitigation Through Exploitation of Structural Instability

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