Estimation of modal parameters of a beam under random excitation using a novel 3D continuously scanning laser Doppler vibrometer system and an extended demodulation method

Abstract

A novel three-dimensional (3D) continuously scanning laser Doppler vibrometer (CSLDV) system that contains three CSLDVs and an external controller is developed to measure 3D vibration of a structure under random excitation, and a new operational modal analysis method is proposed to estimate its 3D modal parameters, including damped natural frequencies and undamped end-to-end mode shapes, by extending the conventional demodulation method. Calibration among three CSLDVs in the 3D CSLDV system based on the geometrical model of its scan mirrors is conducted to adjust their rotational angles and ensure that three laser spots can continuously and synchronously move along the same scan path on the structure. The extended demodulation method can estimate undamped mode shapes of the structure under random excitation by filtering raw response with a bandpass filter and multiplying the filtered response by sinusoidal signals with its damped natural frequencies obtained from the fast Fourier transform of raw response. Experimental investigation on one-dimensional (1D) and 3D CSLDV measurements for modal parameter estimation is conducted on a beam under white-noise excitation to validate the extended demodulation method and examine the accuracy of the 3D CSLDV system. Modal assurance criterion (MAC) values between the first four undamped mode shapes of the beam from 1D CSLDV measurement and corresponding damped mode shapes from 1D step-wise scanning measurement are larger than 95%. MAC values between the first four undamped mode shapes of the beam from 3D CSLDV measurement and corresponding damped mode shapes from 3D step-wise scanning measurement are larger than 90% in all the three directions of a specified measurement coordinate system.