Experimental characterization of a nonlinear vibration absorber using free vibration

Abstract Knowledge of the nonlinear characteristics of a vibration absorber is important if its performance is to be predicted accurately when connected to a host structure. This can be achieved theoretically, but experimental validation is necessary to verify the modelling procedure and assumptions. This paper describes the characterization of such an absorber using a novel experimental procedure. The estimation method is based on a free vibration test, which is appropriate for a lightly damped device. The nonlinear absorber is attached to a shaker which is operated such that the shaker works in its mass-controlled regime, which means that the shaker dynamics, which are also included in the measurement, are considerably simplified, which facilitates a simple estimation of the absorber properties. From the free vibration time history, the instantaneous amplitude and instantaneous damped natural frequency are estimated using the Hilbert transform. The stiffness and damping of the nonlinear vibration absorber are then estimated from these quantities. The results are compared with an analytical solution for the free vibration of the nonlinear system with cubic stiffness and viscous damping, which is also derived in the paper using an alternative approach to the conventional perturbation methods. To further verify the approach, the results are compared with a method in which the internal forces are balanced at each measured instant in time.

[1]  Jian-Qiao Sun,et al.  Passive, Adaptive and Active Tuned Vibration Absorbers—A Survey , 1995 .

[2]  Michael Feldman,et al.  Non-linear system vibration analysis using Hilbert transform--I. Free vibration analysis method 'Freevib' , 1994 .

[3]  I. Kovacic,et al.  The Duffing Equation: Nonlinear Oscillators and their Behaviour , 2011 .

[4]  J. Ormondroyd.  Theory of the Dynamic Vibration Absorber , 1928 .

[5]  Henry J. Rice,et al.  Practical non-linear vibration absorber design , 1987 .

[6]  Robert E. Roberson,et al.  Synthesis of a nonlinear dynamic vibration absorber , 1952 .

[7]  Sami F. Masri,et al.  Theory of the Dynamic Vibration Neutralizer With Motion-Limiting Stops , 1972 .

[8]  G. Kerschen,et al.  Nonlinear Targeted Energy Transfer in Mechanical and Structural Systems , 2008 .

[9]  Michael J. Brennan.  Some recent developments in adaptive tuned vibration absorbers/neutralisers , 2006 .

[10]  S. Natsiavas,et al.  Steady state oscillations and stability of non-linear dynamic vibration absorbers , 1992 .

[11]  Gianluca Gatti,et al.  The characteristics of a nonlinear vibration neutralizer , 2012 .

[12]  G. C. Kung,et al.  Nonlinear Flexural Vibrations of a Clamped Circular Plate , 1972 .

[13]  K. Worden,et al.  Past, present and future of nonlinear system identification in structural dynamics , 2006 .

[14]  Riccardo Riganti.  Subharmonic steady vibrations of a non-linear damper with two degrees of freedom and viscous damping , 1980 .

[15]  K. Mendelson,et al.  Perturbation Theory for Damped Nonlinear Oscillations , 1970 .

[16]  Gaëtan Kerschen,et al.  Nonlinear vibration absorber coupled to a nonlinear primary system: A tuning methodology , 2009 .

[17]  Ali H. Nayfeh,et al.  A review of development and implementation of an active nonlinear vibration absorber , 1999 .

[18]  Henry J. Rice,et al.  Combinational ínstability of the non-linear vibration absorber , 1986 .

[19]  G. Tomlinson,et al.  Nonlinearity in Structural Dynamics: Detection, Identification and Modelling , 2000 .

[20]  S. Timoshenko,et al.  THEORY OF PLATES AND SHELLS , 1959 .

[21]  Bin Tang,et al.  Using nonlinear jumps to estimate cubic stiffness nonlinearity: An experimental study , 2016 .

[22]  Yiming Fu,et al.  Analysis of non-linear dynamics of a two-degree-of-freedom vibration system with non-linear damping and non-linear spring , 2004 .

[23]  Ivan Jordanov,et al.  Optimal design of linear and non-linear dynamic vibration absorbers , 1988 .

[24]  Pekka Vähäoja,et al.  Recent Studies of Adaptive Tuned Vibration Absorbers/Neutralizers , 2009 .

[25]  W. J. Parzygnat,et al.  Resonance phenomena in the nonlinear vibration of plates governed by Duffing's equation , 1978 .

[26]  T. D. Burton.  On the amplitude decay of strongly non-linear damped oscillators , 1983 .

[27]  R. White,et al.  Effects of non-linearity due to large deflections in the derivation of frequency response data from the impulse response of structures , 1973 .