Experimental identification of hardening and softening nonlinearity in circular laminated plates

Abstract This work investigates nonlinear characteristics of a circular laminated plate. A nonparametric identification method based on the Hilbert transform is applied to identify the nonlinear system. The results demonstrate that the force–displacement curve has a soft nonlinear characteristic under small displacements and a hard nonlinear characteristic under large displacements. The force–velocity curve also has a soft nonlinear characteristic. A circular isotropic plate is treated to test the method. The force-state method is adopted to confirm the identification results. The effects of the plate diameter are examined. A combination of a cubic polynomial and a hyperbolic tangent function is proposed to fit the experiment data. The fitting results are verified by time domain simulations under random excitations. The work illustrates some novel nonlinear characteristics in transverse vibration of a circular laminated plate via a nonlinear system identification process.

[1]  William W. Clark,et al.  Piezoelectric Energy Harvesting with a Clamped Circular Plate: Analysis , 2005 .

[2]  William W. Clark,et al.  Piezoelectric Energy Harvesting with a Clamped Circular Plate: Experimental Study , 2005 .

[3]  K. Hedrih.  Double plate system with a discontinuity in the elastic bonding layer , 2007 .

[4]  Zhengbao Yang,et al.  High-efficiency compressive-mode energy harvester enhanced by a multi-stage force amplification mechanism , 2014 .

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

[6]  Balakumar Balachandran,et al.  Sensor diaphragm under initial tension: Nonlinear responses and design implications , 2008 .

[7]  F. Alijani,et al.  Damping for large-amplitude vibrations of plates and curved panels, part 2: Identification and comparisons , 2016 .

[8]  Ying Dong,et al.  Energy harvester array using piezoelectric circular diaphragm for broadband vibration , 2014 .

[9]  Katica R. Hedrih,et al.  Non-linear dynamics of the sandwich double circular plate system , 2010 .

[10]  S. Masri,et al.  Enabling reduced-order data-driven nonlinear identification and modeling through naïve elastic net regularization , 2017 .

[11]  Hao Wu,et al.  Development of a broadband nonlinear two-degree-of-freedom piezoelectric energy harvester , 2014 .

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

[13]  Marco Amabili,et al.  Non-linear vibrations of shells: A literature review from 2003 to 2013 , 2014 .

[14]  Sami F. Masri,et al.  A Nonparametric Identification Technique for Nonlinear Dynamic Problems , 1979 .

[15]  Chengliang Sun,et al.  A novel drum piezoelectric-actuator , 2006 .

[16]  M. Feldman.  Hilbert transform in vibration analysis , 2011 .

[17]  Yang Jian,et al.  Vibration energy harvesting system for railroad safety based on running vehicles , 2014 .

[18]  Michael Feldman,et al.  Non-linear system vibration analysis using Hilbert transform--II. Forced vibration analysis method 'Forcevib' , 1994 .

[19]  S. Masri,et al.  Data-Based Nonlinear Identification and Constitutive Modeling of Hysteresis in NiTiNOL and Steel Strands , 2016 .

[20]  A. Erturk,et al.  On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion , 2014 .

[21]  Tao Xie,et al.  Performance of a Drum Transducer for Scavenging Vibration Energy , 2009 .

[22]  M. Feldman.  Mapping nonlinear forces with congruent vibration functions , 2013 .

[23]  Balakumar Balachandran,et al.  Experimental Verification of the Importance of The Nonlinear Curvature in the Response of a Cantilever Beam , 1994 .

[24]  Xingzhong Zhao,et al.  Energy harvesting with piezoelectric drum transducer , 2007 .

[25]  Michael Feldman,et al.  Decomposition of non-stationary signals into varying time scales: Some aspects of the EMD and HVD methods , 2011 .

[26]  Li-Qun Chen,et al.  Internal Resonance Energy Harvesting , 2015 .

[27]  A. Dobrucki,et al.  Theory of piezoelectric axisymmetric bimorph , 1997 .

[28]  Marco Amabili,et al.  Damping for large-amplitude vibrations of plates and curved panels, Part 1: Modeling and experiments , 2016 .

[29]  Keith Worden,et al.  Nonlinear system identification of automotive dampers: A time and frequency-domain analysis , 2009 .

[30]  Balakumar Balachandran,et al.  Parametric identification of piezoelectric microscale resonators , 2006 .

[31]  K. Hedrih,et al.  Multi-frequency analysis of the double circular plate system non-linear dynamics , 2012 .