Investigation of three-dimensional vibration measurement by a single scanning laser Doppler vibrometer

A scanning laser Doppler vibrometer (SLDV) has been widely used in non-contact vibration measurement. This paper presents a novel investigation of three-dimensional (3D) vibration measurement by a single SLDV sequentially placed at three different positions, where 3D vibration is defined as three vibration components along axes of a specified measurement coordinate system (MCS), which can give more precise knowledge of structural dynamic characteristics. A geometric model of the SLDV is proposed and a vibrometer coordinate system (VCS) based on the geometric model is defined and fixed on the SLDV. The pose of a SLDV with respect to a MCS is expressed in the form of a translation vector and a direction cosine matrix from the VCS to the MCS, which can be calculated by four or more target points with known coordinates in both the MCS and the VCS. An improved method based on the least squares method and singular value decomposition is proposed to obtain the pose of the SLDV. Compared with an inverse method, the proposed method can yield an orthogonal direction cosine matrix and be applicable to a two-dimensional structure. Effects of the number of target points on the accuracy and stability of the proposed method are investigated. With three direction cosine matrices of three different positions obtained by the proposed method, measured vibration velocities along laser line-of-sight directions can be transformed to vibration components along axes of the MCS. An experiment was conducted to measure 3D vibration of a target point on a beam under sinusoidal excitation by a single SLDV sequentially placed at three different positions. Vibration components along axes of the MCS obtained by the single SLDV were in good agreement with those from a commercial Polytec 3D scanning laser vibrometer PSV-500-3D.