Flexural Vibration Measurement and Sound Radiation Estimate of Thin Structures with Multiple Cameras

This thesis presents a simulation and experimental study focussed on the measurement of flexural vibration and on the estimate of the sound radiation of distributed structures by optical means and in particular by using multiple, i.e. more than two, synchronous cameras. The study considers two model problems composed by a cantilever beam and a plate excited by a tonal force at the first three fundamental resonance frequencies of flexural vibrations. The study has therefore considered the measurement of the deflection shapes at these frequencies, which accurately approximates the first three flexural mode shapes. The study is organized in four parts. The first part introduces the state of the art about the topic and revises the theoretical principles concerning optical measurements. The second part presents a simplified optical model employed to simulate how the accuracy of the measurements of the first three flexural deflection shapes of the structures here considered varies with respect to: a) the distance of the cameras from the structure; b) the angle of aperture between pairs of cameras; c) the elevation angle formed by the optical axis of the camera and the plane of the structure; d) the resolution of the cameras and e) the number of cameras. The principal objective of the study was indeed to show how the accuracy of the measurements can be significantly increased by using multiple cameras. The third part of the study provided experimental results taken on a beam rig and camera setup assembled using off-the-shelf devices. The experimental study focussed on the first flexural deflection shape of a cantilever beam and confirmed the findings of the simulation studies. The simulations and experiments presented in this work, quantify and confirm that the use of multiple cameras allows good vibration measurement accuracy, even at low spatial camera resolutions. Since the frame-rate and cost of cameras is limited by the amount of data they can process in each time unit, these results suggest that multiple, relatively cheap, high-speed, low-spatial resolution cameras can be used to perform vibration measurements in practical applications. The fourth part of the study examines the sound radiation generated by vibrating structures. In particular, it is evaluated how the accuracy of the estimate of the sound radiation emitted by the reconstructed first three flexural deflection shapes of a plate varies with respect to: a) the distance of the cameras from the structure; b) the azimuthal angle between the cameras; c) the elevation angle of the cameras; d) the resolution of cameras and e) the number of cameras. The principal objective of this fourth part was to understand if the results obtained on the influence on the flexural vibration measurements of the parameters listed above, could be applied to the case study of the estimate of the sound radiation.