Multi-view videogrammetry for the measurement of plate flexural vibration

This paper describes a simulation study of the measurement of the flexural deflection of a thin plate, excited by a transverse force at the fundamental frequency of the resonance modes, using an optical system consisting of multiple cameras. The estimate of the amplitude of the vibration is obtained starting from two or more sequences of images taken by the cameras, by means of triangulation. In this paper, we assume that the system is calibrated, and we focus on the error resulting from pixellisation. The simplified optical model is used to simulate how the accuracy of the measurements varies with respect to: the distance of the cameras from the structure; the opening angle between pairs of cameras; the resolution of the cameras and their number. The aim of the work is to evaluate the influence of the cameras arrangement on the measurement quality, and in particular if the use of a number greater than 2 cameras can allow a reduction of the measurement error, allowing a favorable compromise between spatial and temporal resolution of the cameras. As an example, the average error of the reconstruction of the first flexural deflection shape falls from 12% to 4%, when the measurement setup passes from 2 cameras to 12 cameras in the considered setup.