Full field modal measurement with a single standard camera

Abstract The full field measurement of 8 vibration modes of a cantilever plate, up to the kHz frequency is performed using a single standard camera. The image acquisition is carried out at low rate but using fast exposure time (1/4000 s) that “freezes” a part of the motion. A deflectometry setup coupled with digital image correlation analysis allows angle fields, then deflection fields, to be measured. An out–of–plane displacement database is generated from all stored fields. This snapshot library is finally post-processed using principal component analysis techniques and adapted weights that enable space vibration fields to be extracted. A test case is performed on a reflecting cantilever steel plate. 370 deflection fields are measured allowing 8 space vibration fields to be extracted. The natural frequencies of those modes are estimated using the Rayleigh ratio. A coarse and visual comparison with a numerical simulation shows similar results for 6 of the 8 space modes.

[1]  Stéphane Roux,et al.  Big Data in Experimental Mechanics and Model Order Reduction: Today’s Challenges and Tomorrow’s Opportunities , 2017, Archives of Computational Methods in Engineering.

[2]  Fabrice Pierron,et al.  Stiffness and Damping Identification from Full Field Measurements on Vibrating Plates , 2006 .

[3]  Jan Burke,et al.  Qualifying parabolic mirrors with deflectometry , 2013 .

[4]  François Hild,et al.  A space–time approach in digital image correlation: Movie-DIC , 2011 .

[5]  Stéphane Roux,et al.  Shape, displacement and mechanical properties from isogeometric multiview stereocorrelation , 2015 .

[6]  P. Glynne-Jones,et al.  Time-resolved full-field imaging of ultrasonic Lamb waves using deflectometry , 2016 .

[7]  Stéphane Roux,et al.  Toward 4D mechanical correlation , 2016, Adv. Model. Simul. Eng. Sci..

[8]  Stéphane Roux,et al.  Estimation of Elastoplastic Parameters via Weighted FEMU and Integrated-DIC , 2015 .

[9]  Daniel P. Rohe,et al.  Comparison of DIC and LDV for practical vibration and modal measurements , 2017 .

[10]  T. Lumley,et al.  PRINCIPAL COMPONENT ANALYSIS AND FACTOR ANALYSIS , 2004, Statistical Methods for Biomedical Research.

[11]  T. Siebert,et al.  Vibration Analysis using 3D Image Correlation Technique , 2010 .

[12]  Michael A. Sutton,et al.  Computer Vision-Based, Noncontacting Deformation Measurements in Mechanics: A Generational Transformation , 2013 .

[13]  Katia Genovese,et al.  Stereo-Digital Image Correlation (DIC) measurements with a single camera using a biprism , 2013 .

[14]  D. Harris,et al.  Surface topography measurements of the bouncing droplet experiment , 2016 .

[15]  Edwin Kreuzer,et al.  Analysis of long torsional strings by proper orthogonal decomposition , 1996 .

[16]  B. Feeny,et al.  Interpreting proper orthogonal modes of randomly excited vibration systems , 2003 .

[17]  Martin Hagara,et al.  The Measurement of Standing Wave Patterns by using High-speed Digital Image Correlation , 2014 .

[18]  François Hild,et al.  Mesh-Based Shape Measurements with Stereocorrelation , 2016 .

[19]  Run Huang High precision optical surface metrology using deflectometry , 2015 .

[20]  Stéphane Roux,et al.  3D surface measurements with isogeometric stereocorrelation—Application to complex shapes , 2016 .

[21]  M. Rabaud,et al.  A synthetic Schlieren method for the measurement of the topography of a liquid interface , 2009 .

[22]  Peter Avitabile,et al.  A Review of Digital Image Correlation Applied to Structura Dynamics , 2010 .

[23]  Stéphane Roux,et al.  Integrated Digital Image Correlation considering gray level and blur variations: Application to distortion measurements of IR camera , 2016 .

[24]  Bing Pan,et al.  Single-camera high-speed stereo-digital image correlation for full-field vibration measurement , 2017 .

[25]  S. Roux,et al.  Digital image correlation and fracture: an advanced technique for estimating stress intensity factors of 2D and 3D cracks , 2009 .

[26]  M. Wisnom,et al.  Damage detection in composite materials using deflectometry, a full-field slope measurement technique , 2012 .

[27]  B. Feeny,et al.  On the physical interpretation of proper orthogonal modes in vibrations , 1998 .

[28]  G. Kerschen,et al.  The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview , 2005 .

[29]  Bo Gao,et al.  Modal phase measuring deflectometry. , 2016, Optics express.

[30]  H. Abdi,et al.  Principal component analysis , 2010 .

[31]  James H. Burge,et al.  Measuring large mirrors using SCOTS: the Software Configurable Optical Test System , 2014, Astronomical Telescopes and Instrumentation.

[32]  S. Roux,et al.  Comparison of Local and Global Approaches to Digital Image Correlation , 2012 .

[33]  Qianbing Zhang,et al.  Review of single-camera stereo-digital image correlation techniques for full-field 3D shape and deformation measurement , 2018 .

[34]  Qican Zhang,et al.  Optical fringe-reflection deflectometry with sparse representation , 2017 .