MR Damper Controlled Vibration Absorber for Enhanced Mitigation of Harmonic Vibrations
2. Concept of MR-SVA
2.1. Control Objectives
- its controlled frequency is equal to the actual frequency of vibration at all instants, and
- its controlled damping is minimized under the constraint that the relative motion amplitude of the absorber mass must not be greater than its maximum tolerable value.
2.2. Real-Time Frequency and Damping Controls with MR Damper
- a controllable stiffness force to tune the controllable frequency of the MR-SVA to the actual frequency of vibration, and
- a controllable damping force to minimize the damping and control the relative motion amplitude of the absorber mass.
- zero stiffness when the disturbing frequency is equal to the targeted eigenfrequency of the primary structure, i.e., , whereby the controlled frequency of the MR-SVA is equal to , i.e., .
- positive stiffness if in order to augment the total stiffness of the MR-SVA that is the sum of the passive spring stiffness and the controlled stiffness emulated by the MR damper to generate .
- negative stiffness if in order to diminish the total stiffness of the MR-SVA to produce .
2.3. Control Based on Measured Collocated Displacement
2.4. MR Damper Force Tracking Control Scheme
3. Control Algorithm
3.1. Stiffness of Passive Spring
3.2. Controlled Frequency
3.3. Controlled Adaptive Damping
3.4. Desired Semi-Active Control Force
3.5. Actual Semi-Active Control Force
3.6. Stiffness Correction Method For Precise Frequency Control
3.7. Compromise Solution for Stiffness Correction Method
4. Numerical Validation
4.1. Assessment Criterion
4.2. Assessment of MR-SVA for Tuned and De-Tuned Cases
- The prototype MR-SVA is a mock-up MR-SVA that is designed for a laboratory scale bridge which explains that and are small while and are high compared to values of real mass dampers in big structures. Detailed information on the mock-up MR-SVA and the laboratory scale bridge is available in Section 5.1.
- The experimental validation of the prototype MR-SVA is performed with a suboptimally tuned as the passive mass spring packet of the MR-SVA was originally designed to assess the semi-active TMD concept of the Volgograd Bridge, Russia [2,3,18,21], which required to design according to the design of TMDs for minimum structural displacement , i.e., .
4.3. Levels of Excitation
- Maximum excitation : The maximum excitation force amplitude evokes whereby the desired damping of the MR-SVA is equal to its nominal value . For higher levels of excitation, i.e., , the normalized displacement response given by Equation (16) does not change since the damping gain = 1 for does not change the desired damping, see Equation (9).
- Excitation : The excitation force amplitude results in whereby the desired damping of the MR-SVA is equal to its minimum value . For lower levels of excitation, i.e., , the normalized displacement response given by Equation (16) does not change as the damping gain for is constant, see Equation (9).
- Excitation : The excitation force amplitude is selected to be slightly smaller than the worst-case excitation , i.e., , to show the significant vibration reduction improvement when the excitation is approx. 80% to 90% of worst case excitation .
4.5. Dynamic Simulation
4.6. Numerical Results
- : If the damping of the MR-SVA cannot be reduced by the adaptive nonlinear damping control approach Equations (5)–(9) because the relative motion amplitude of the damper mass is equal to the normalized displacement due to the MR-SVA is equal to that of the passive TMD; this occurs at equal to the natural frequency of the TMD, i.e., , since then the frequency tunings and—because of —also the damping tunings of the TMD and MR-SVA are the same.
- : If the damping of the MR-SVA can be reduced by the adaptive nonlinear damping control approach Equations (5)–(9) due to the MR-SVA leads to significantly smaller normalized displacements than the passive TMD because
- the reduced damping augments and thereby increases the amplitude of the MR-SVA stiffness force, and
- the frequency control generates the targeted phase shift of 180 degrees between the MR-SVA stiffness force and the excitation force,
- The normalized displacement response due to the MR-SVA with = 2 N and for shows two maxima at approx. 2.9 Hz and 3.4 Hz because the actual, i.e., energy equivalent viscous damping coefficient is greater than its desired counterpart at these frequencies which diminishes the stiffness force amplitude of the MR-SVA and, as a result, lowers the compensation of the disturbing force.
- The simulation of the MR-SVA with negligible small residual force ( = 0 N) of the MR damper representing an ideal semi-active control force range cancels the oscillations of the primary structure at since then the MR-SVA precisely emulates the behaviour of the undamped dynamic vibration absorber. For excitation frequencies the MR-SVA cannot generate the behaviour of the undamped dynamic vibration absorber because the stiffness emulation by the MR damper force to generate the frequency control of the MR-SVA can only be realized in combination with a dissipative force whereby undesired damping is generated. Only with active vibration absorbers it is possible to emulate the behaviour of the undamped dynamic vibration absorber for any disturbing frequency .
5. Experimental Validation
5.1. Test Set-Up
5.2. Force Tracking Control Scheme
5.3. Experimental Results
6. MR-SVA of Danube City Tower in Vienna
6.1. Project Description
6.2. Hybrid Testing
6.3. Accurate Force Tracking Control within 1 Day
6.4. MR-SVA with Reduced Mass
7. Summary and Conclusions
Conflicts of Interest
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|Tuned Case||De-Tuned Cases|
|Prototype MR-SVA||Nominal Primary Structure||Eigenfrequency Change||Eigenfrequency||DampingRatio|
|= 3.15 Hz (simulation)||= 3.15 Hz||+5%||= 3.31 Hz||0.52%|
|= 3.10 Hz (tests)||= 1680 kg||+10%||= 3.46 Hz||0.51%|
|= 26.325 kg||= 658.1 kN/m||−5%||= 2.99 Hz||0.48%|
|= 2 N (simulation)||= 0.40%||−10%||= 2.84 Hz||0.49%|
|2, …, 4 N (tests)|
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Weber, F.; Distl, H.; Fischer, S.; Braun, C. MR Damper Controlled Vibration Absorber for Enhanced Mitigation of Harmonic Vibrations. Actuators 2016, 5, 27. https://doi.org/10.3390/act5040027
Weber F, Distl H, Fischer S, Braun C. MR Damper Controlled Vibration Absorber for Enhanced Mitigation of Harmonic Vibrations. Actuators. 2016; 5(4):27. https://doi.org/10.3390/act5040027Chicago/Turabian Style
Weber, Felix, Hans Distl, Sebastian Fischer, and Christian Braun. 2016. "MR Damper Controlled Vibration Absorber for Enhanced Mitigation of Harmonic Vibrations" Actuators 5, no. 4: 27. https://doi.org/10.3390/act5040027