Robust Skewness-Kurtosis Descriptor for Damping Calibration from Frequency Response

AbstractThis paper attempts to define simple, consistent, and robust statistical descriptors for the calibration of damping in linear and nonlinear systems through the frequency response in the presence of variability and uncertainties as a result of noise and sampling intervals. The work uses the frequency response of a linear system and a Duffing oscillator simulating hardening and softening springs. The skewness-kurtosis descriptor was observed to be efficiently calibrating the nature of the system and the extent of damping with robustness against the measurement noise and sampling effects. The descriptors allow rapid computation and can be applied to experimental data without the requirement of assuming a specific underlying model. The findings are general and applicable to a very broad spectrum of linear and nonlinear systems and applications.

[1]  Neil D. Sims,et al.  Energy harvesting from the nonlinear oscillations of magnetic levitation , 2009 .

[2]  Leontios J. Hadjileontiadis,et al.  Crack detection in beams using kurtosis , 2005 .

[3]  Vikram Pakrashi,et al.  Nondetection, False Alarm, and Calibration Insensitivity in Kurtosis- and Pseudofractal-Based Singularity Detection , 2009 .

[4]  H. Yin,et al.  An average inverse power ratio method for the damping estimation from a frequency response function , 2010 .

[5]  S. Billings,et al.  Analysis of bilinear oscillators under harmonic loading using nonlinear output frequency response functions , 2007 .

[6]  Mallik,et al.  Role of nonlinear dissipation in soft Duffing oscillators. , 1994, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[7]  A. Sarkar,et al.  Nonlinear filters for chaotic oscillatory systems , 2009 .

[8]  Biswajit Basu,et al.  A Statistical Measure for Wavelet Based Singularity Detection , 2009 .

[9]  Frank T. Fisher,et al.  A coupled piezoelectric–electromagnetic energy harvesting technique for achieving increased power output through damping matching , 2009 .

[10]  Leontios J. Hadjileontiadis,et al.  Kurtosis analysis for crack detection in thin isotropic rectangular plates , 2007 .

[11]  R. Clough,et al.  Dynamics Of Structures , 1975 .

[12]  C. Lamarque,et al.  DAMPING IDENTIFICATION IN MULTI-DEGREE-OF-FREEDOM SYSTEMS VIA A WAVELET-LOGARITHMIC DECREMENT—PART 1: THEORY , 2000 .

[13]  Alessandro Carrella.  Passive Vibration Isolators with High-Static-Low-Dynamic-Stiffness , 2010 .

[14]  N. Aluru,et al.  Complex nonlinear oscillations in electrostatically actuated microstructures , 2006, Journal of Microelectromechanical Systems.

[15]  John E. Mottershead,et al.  An assessment of damping identification methods , 2009 .

[16]  Michael I. Friswell,et al.  Piezoelectric energy harvesting with parametric uncertainty , 2010 .

[17]  Approximation of the Duffing oscillator frequency response function using the FPK equation , 2009 .

[18]  Robert G. Parker,et al.  Duffing Oscillator With Parametric Excitation : Analytical and Experimental Investigation on a Belt-Pulley System , 2008 .

[19]  Vikram Pakrashi,et al.  Structural damage detection and calibration using a wavelet-kurtosis technique , 2007 .

[20]  Denis Duhamel,et al.  Natural frequencies and damping estimation using wavelet transform of a frequency response function , 2004 .