Experimental chaotic quantification in bistable vortex induced vibration systems

Abstract The study of energy harvesting by means of vortex induced vibration systems has been initiated a few years ago and it is considered to be potential as a low water current energy source. The energy harvester is realized by exposing an elastically supported blunt structure under water flow. However, it is realized that the system will only perform at a limited operating range (water flow) that is attributed to the resonance phenomenon that occurs only at a frequency that corresponds to the fluid flow. An introduction of nonlinear elements seems to be a prominent solution to overcome the problem. Among many nonlinear elements, a bistable spring is known to be able to improve the harvested power by a vortex induced vibrations (VIV) based energy converter at the low velocity water flows. However, it is also observed that chaotic vibrations will occur at different operating ranges that will erratically diminish the harvested power and cause a difficulty in controlling the system that is due to the unpredictability in motions of the VIV structure. In order to design a bistable VIV energy converter with improved harvested power and minimum negative effect of chaotic vibrations, the bifurcation map of the system for varying governing parameters is highly on demand. In this study, chaotic vibrations of a VIV energy converter enhanced by a bistable stiffness element are quantified in a wide range of the governing parameters, i.e. damping and bistable gap. Chaotic vibrations of the bistable VIV energy converter are simulated by utilization of a wake oscillator model and quantified based on the calculation of the Lyapunov exponent. Ultimately, a series of experiments of the system in a water tunnel, facilitated by a computer-based force-feedback testing platform, is carried out to validate the existence of chaotic responses. The main challenge in dealing with experimental data is in distinguishing chaotic response from noise-contaminated periodic responses as noise will smear out the regularity of periodic responses. For this purpose, a surrogate data test is used in order to check the hypotheses for the presence of chaotic behavior. The analyses from the experimental results support the hypothesis from simulation that chaotic response is likely occur on the real system.

[1]  C. Williamson,et al.  DYNAMICS OF A HYDROELASTIC CYLINDER WITH VERY LOW MASS AND DAMPING , 1996 .

[2]  Luis A. R. Quadrante,et al.  Attachment of Tripping Wires to Enhance the Efficiency of a Vortex-Induced Vibrations Energy Generation System , 2013 .

[3]  Anoshirvan Farshidianfar,et al.  Modified higher-order wake oscillator model for vortex-induced vibration of circular cylinders , 2013 .

[4]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[5]  I. Kovacic,et al.  Potential benefits of a non-linear stiffness in an energy harvesting device , 2010 .

[6]  L. Cao.  Practical method for determining the minimum embedding dimension of a scalar time series , 1997 .

[7]  Turgut Sarpkaya,et al.  A critical review of the intrinsic nature of vortex-induced vibrations , 2004 .

[8]  Abhijit Sarkar,et al.  Lumped parameter models of vortex induced vibration with application to the design of aquatic energy harvester , 2013 .

[9]  Just L. Herder,et al.  Bistable vibration energy harvesters: A review , 2013 .

[10]  Ryan L. Harne,et al.  A review of the recent research on vibration energy harvesting via bistable systems , 2013 .

[11]  Y. Wang,et al.  Nonlinearly enhanced vortex induced vibrations for energy harvesting , 2015, 2015 IEEE International Conference on Advanced Intelligent Mechatronics (AIM).

[12]  Charles H. K. Williamson,et al.  Developing a cyber-physical fluid dynamics facility for fluid–structure interaction studies , 2011 .

[13]  John Sheridan,et al.  Chaotic vortex induced vibrations , 2014 .

[14]  Kamaldev Raghavan,et al.  VIVACE (Vortex Induced Vibration Aquatic Clean Energy): A New Concept in Generation of Clean and Renewable Energy From Fluid Flow , 2008 .

[15]  Tegoeh Tjahjowidodo,et al.  Theoretical analysis of the dynamic behavior of presliding rolling friction via skeleton technique , 2012 .

[16]  Ulrich Parlitz,et al.  Nonlinear Time-Series Analysis , 1998 .

[17]  S. Strogatz.  Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry and Engineering , 1995 .

[18]  Johan A. K. Suykens,et al.  Nonlinear modeling : advanced black-box techniques , 1998 .

[19]  Tegoeh Tjahjowidodo,et al.  Non-local memory hysteresis in a pneumatic artificial muscle (PAM) , 2009, 2009 17th Mediterranean Conference on Control and Automation.

[20]  Andrzej Stefański,et al.  Estimation of the largest Lyapunov exponent in systems with impacts , 2000 .

[21]  Tegoeh Tjahjowidodo,et al.  An investigation of friction-based tendon sheath model appropriate for control purposes , 2014 .

[22]  Haym Benaroya,et al.  An overview of modeling and experiments of vortex-induced vibration of circular cylinders , 2005 .

[23]  Michael M. Bernitsas,et al.  Virtual damper-spring system for VIV experiments and hydrokinetic energy conversion , 2011 .

[24]  Hendrik Van Brussel,et al.  Quantifying chaotic responses of mechanical systems with backlash component , 2007 .

[25]  Henry D. I. Abarbanel,et al.  Analysis of Observed Chaotic Data , 1995 .

[26]  Tomasz Kapitaniak,et al.  Estimation of the dominant Lyapunov exponent of non-smooth systems on the basis of maps synchronization , 2003 .

[27]  E. de Langre,et al.  Coupling of Structure and Wake Oscillators in Vortex-Induced Vibrations , 2004 .

[28]  C. Williamson,et al.  Vortex-Induced Vibrations , 2004, Wind Effects on Structures.

[29]  Robert C. Hilborn,et al.  Chaos And Nonlinear Dynamics: An Introduction for Scientists and Engineers , 1994 .

[30]  H. Van Brussel,et al.  Non-linear dynamics tools for the motion analysis and condition monitoring of robot joints , 2001 .

[31]  Santiago Pindado,et al.  Extracting energy from Vortex-Induced Vibrations: A parametric study , 2012 .

[32]  T. Schreiber,et al.  Surrogate time series , 1999, chao-dyn/9909037.

[33]  Michael M. Bernitsas,et al.  Enhancement of flow-induced motion of rigid circular cylinder on springs by localized surface roughness at 3×104≤Re≤1.2×105 , 2013 .

[34]  Jean-Marc Chomaz,et al.  An asymptotic expansion for the vortex-induced vibrations of a circular cylinder , 2011, Journal of Fluid Mechanics.

[35]  M. Bernitsas,et al.  Hydrokinetic Energy Harnessing Using the VIVACE Converter With Passive Turbulence Control , 2011 .

[36]  Charles H. K. Williamson,et al.  An experimental investigation of vortex-induced vibration with nonlinear restoring forces , 2013 .

[37]  Hugh Maurice Blackburn,et al.  Lock-in behavior in simulated vortex-induced vibration , 1996 .

[38]  Michael S. Triantafyllou,et al.  Combined Simulation with Real-Time Force Feedback: A New Tool for Experimental Fluid Mechanics , 2000 .

[39]  Tomasz Kapitaniak,et al.  Evaluation of the largest Lyapunov exponent in dynamical systems with time delay , 2005 .

[40]  Charles H. K. Williamson,et al.  Investigation of relative effects of mass and damping in vortex-induced vibration of a circular cylinder , 1997 .

[41]  Chee Kiong Soh,et al.  Broadband Vibration Energy Harvesting Techniques , 2013 .

[42]  P. Perdikaris,et al.  Chaos in a cylinder wake due to forcing at the Strouhal frequency , 2009 .

[43]  C. Williamson,et al.  MOTIONS, FORCES AND MODE TRANSITIONS IN VORTEX-INDUCED VIBRATIONS AT LOW MASS-DAMPING , 1999 .

[44]  Tegoeh Tjahjowidodo,et al.  Structural response investigation of a triangular-based piezoelectric drive mechanism to hysteresis effect of the piezoelectric actuator , 2013 .

[45]  F. Al-Bender,et al.  Experimental dynamic identification of backlash using skeleton methods , 2007 .