Modal identification of vibrating structures using singular value decomposition and nonlinear iteration based on high-speed digital image correlation

摘要

This study aims to develop an effective method to identifying modal parameters of vibrating structures using digital image correlation (DIC) technique, in which singular value decomposition (SVD) and nonlinear least square iteration are integrated. The proposed approach was first used to measure modal parameters of a cantilever plate to verify its effectiveness and accuracy. The obtained results were compared with those measured with the forced normal mode test, operating deflection shape measurement, accelerometer, Laser Doppler Vibrometer and finite element techniques. In the experiment, synchronization of the hammer hitting and high-speed camera signals was achieved via the data acquisition cards and Labview program. Natural frequency and damping ratios were obtained through the enhanced frequency response functions with a nonlinear least square algorithm; and the mode shapes were determined through singular value decomposition. The experimental modal parameters of the cantilever plate identified by the present method agreed well with those identified by the Polymax modal estimator in the commercial code LMS test.lab and rational fraction polynomial. It is demonstrated that use of DIC technique for vibration analysis is of considerable advantages in comparison with the accelerometer and LDV techniques. Finally, a real-life case study was performed for vibratory modal analysis of a passenger car bonnet in this study. It is shown that the experimental modal parameters of the real car bonnet identified by the present method agreed well with those identified by the forced normal mode and the accelerometer tests. The proposed technique is anticipated to provide an effective approach for identification of modal parameters of vibrating structures in practical applications.This study aims to develop an effective method to identifying modal parameters of vibrating structures using digital image correlation (DIC) technique, in which singular value decomposition (SVD) and nonlinear least square iteration are integrated. The proposed approach was first used to measure modal parameters of a cantilever plate to verify its effectiveness and accuracy. The obtained results were compared with those measured with the forced normal mode test, operating deflection shape measurement, accelerometer, Laser Doppler Vibrometer and finite element techniques. In the experiment, synchronization of the hammer hitting and high-speed camera signals was achieved via the data acquisition cards and Labview program. Natural frequency and damping ratios were obtained through the enhanced frequency response functions with a nonlinear least square algorithm; and the mode shapes were determined through singular value decomposition. The experimental modal parameters of the cantilever plate identified by the present method agreed well with those identified by the Polymax modal estimator in the commercial code LMS test.lab and rational fraction polynomial. It is demonstrated that use of DIC technique for vibration analysis is of considerable advantages in comparison with the accelerometer and LDV techniques. Finally, a real-life case study was performed for vibratory modal analysis of a passenger car bonnet in this study. It is shown that the experimental modal parameters of the real car bonnet identified by the present method agreed well with those identified by the forced normal mode and the accelerometer tests. The proposed technique is anticipated to provide an effective approach for identification of modal parameters of vibrating structures in practical applications.