Tribomechadynamics Research Camp
Rice University, Houston TX
June 25
th– August 2
nd, 2019
http://tmd.rice.edu
Comparison Between Control-Based Continuation and Phase-Locked Loop Methods
for the Identification of Backbone Curves and Nonlinear Frequency Responses
Motivation
F. Müller, G. Abeloos, E. Ferhatoglu, M. Scheel, M. Brake, P. Tiso, L. Renson, M. Krack
Experimental Setup
Phase-Locked Loop (PLL)
Conclusions
References
• Model-less experimental characterization of
nonlinear structures with PLL and CBC
Backbone Curves
Nonlinear Frequency Responses
• No direct comparison of the methods has
been performed until now
[1] Scheel, M., Peter, S., Leine, R. I., & Krack, M. (2018). A phase resonance approach for modal testing of structures with nonlinear dissipation. Journal of Sound and
Vibration, 435, 56-73.
[2] Peter, S., & Leine, R. I. (2017). Excitation power quantities in phase resonance testing of nonlinear systems with phase-locked-loop excitation. Mechanical Systems and Signal
Processing, 96, 139-158.
[3] Renson, L., Gonzalez-Buelga, A., Barton, D. A. W., & Neild, S. A. (2016). Robust identification of backbone curves using control-based continuation. Journal of Sound
and Vibration, 367, 145-158.
[4] Renson, L., Barton, D. A., & Neild, S. A. (2017). Experimental tracking of limit-point bifurcations and backbone curves using control-based continuation. International
Journal of Bifurcation and Chaos, 27(01), 1730002.
• Clamped-clamped
curved beam
• Base excitation
• Velocity measured
by laser
• Force measured by
impedance head
Laser
Impedance
head
Beam
Frame
Shaker
312 312.5 313 313.5 314 314.5 315 315.5 Excitation Frequency [Hz] 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 R es po ns e A m pl itu de [m /s ]Nonlinear Frequency Responses
F = 1 N F = 2 N F = 3 N F = 4 N F = 5 N Backbone 0 0.1 0.2 0.3 0.4 0.5 0.6 Response Amplitude [m/s] 0 0.02 0.04 0.06 0.08 0.1 0.12 D am pi ng R at io [% ] 313 314 315 316 317 318 319 320 R es on an ce F re qu en cy n l [H z]
Change of Modal Properties of the First Mode
Linear Damping
(EMA)
n l
Nonlinear Damping
• Response amplitude is imposed by a PD controller Control is made non-invasive by Picard iterations Measured excitation force is made
mono-harmonic by Newton iterations
• Backbone curves are obtained by increasing the response amplitude and tuning the excitation frequency until the quadrature of phase
• S-curves are obtained by increasing the response amplitude at constant excitation frequency
• The full dynamics manifold is constructed by minimizing the distance between a Bézier surface and S-curves data points
Control-Based Continuation (CBC)
312 313 314 315 316 317 318 Frequency [Hz] 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5 R es po ns e A m p lit ud e [m /s ] Backbone Curves CBC PLL• Backbones obtained by both methods are consistent
• Nonlinear frequency response curves can be obtained by both methods
• Higher forcing harmonics can be cancelled with both methods
• Further studies could focus on: comparison of performance more complex nonlinearities
• Phaselag between excitation (=force) and response (=velocity) is evaluated online and controlled to a specific value
Stepping from low to high excitation amplitude at phaselag = 0°yields backbone curve
Stepping through phaselag at constant excitation amplitude yields frequency response including instable branches
• From the backbone measurement results:
amplitude dependent damping is calculated frequency response is synthesized
Excitation Frequency [Hz] R e sp o ns e A m p lit ud e [m /s ]
