Dynamic Frame Based Exercises
Using 3 absorbers to reduce all three resonances
In the vibration absorber short lab you have looked at the effect of adding a tuned mass damper (TMD) to the structure to reduce the amplitude of vibration at resonance. The aim of this extended exercise is to tune 3 vibration absorbers to damp out all three resonances on the model structure (by adding one to each floor). The first stage of this experiment will involve testing your predictions from the short lab on the model structures to verify the calculated solution. In the South Wing lab you will find various threaded rods and small masses that can be attached to each floor.
It is suggested that you attempt the following series of tasks; you might not have time to do all of them, so you will have to choose which aspects to focus on:
- Test the vibration absorber design from the short lab on the model structure. How well do your predictions compare with the measured results?
- Tune an absorber at each floor to respond to a different natural frequency of the building. How does the building now behave in response to harmonic loading?
- What is the response of the new system to an impulse or step response? Are tuned mass dampers a good way of dealing with transient vibration?
- How can you adjust the damping of each absorber?
- Typically, you might find that although the vibration is damped significantly at the resonant frequency, there are significant peaks to either side of the old resonance. If instead of tuning one TMD to each mode, the task instead is to look at one mode and reduce that as much as possible, how can you achieve this?
Investigating the effect of additional mass
The final question on the Vibration Modes experiment was to suggest what the effect of an additional floor mass would be. This extended exercise involves making more detailed predictions of changes arising from changes to the mass distribution and comparing these with experiments. You may wish to investigate the effects of this on the structures in the South Wing, or on the shaking tables, or you might want to compare the two.
The short labs use a structure where each floor has an identical mass; this may not be the case in reality.
- Carry out a range of dynamic tests with varying floor masses. Additional masses can be bolted onto each floor.
- For each case, calculate the theoretical natural frequencies of the system. There is some assistance with this provided - remember to use the 4 degree of freedom system if you are conducting the experiment on the shaking tables, and a 3 degree system for the structures in the South Wing.
- How well does the experimental data agree with the theoretical natural frequencies? For the South Wing structures, you can look at both impulse and harmonic loading.
- What about the damping ratio for each mode? Does the extra mass make a large difference? Why do you think this might be?
- Where does your data suggest the safest place for a heavy load in a building might be? Does this agree with common practise?
M-file code for analysing the system
Buckling via vibration modes
One way to detect the approach to buckling is to track natural frequencies: the buckling threshold occurs when a frequency first reaches zero. Why is this so? Investigate the variation of natural frequencies as weights are added to the floors of the building and use this to predict the buckling load. How does it vary depending on the floor to which you add the weights?
Damping rate of the vibration absorber
The theoretical model of a vibration absorber that you analysed in the short lab used a system characterised by three parameters: mass, stiffness and damping rate. Although the mass and spring models seem quite realistic (a rod in bending, at least for small amplitudes, behaves acording to Hooke's law, and the assumption of constant mass is probably ok) there is no obvious reason why the damping should behave like an idealised viscous dashpot. In this extended exercise, you are asked to investigate the validity of this assumption; you may wish to investigate some or all of the following questions, and some extra ones of your own:
- Tune an absorber to match the frequency of a resonance on the structure. How can you measure the damping rate?
- Does the damping in this absorber behave like the assumed viscous dashpot? Is its behaviour linear (i.e. does the damping rate depend on amplitude)? Does it vary with frequency?
- What factors affect the damping rate of the absorber? How can you modify this rate? (Tighter/looser connection? blu-tack?) How can you test the contribution of various effects to the damping?
© Cambridge University, Engineering Department
Last updated 8/1/2013 by hrs@eng