Camera-based mode shape measurements and identification for axially moving objects

Axially moving strings are a fundamental mechanical model in engineering, and their dynamic behaviors, such as vibration modes, have been extensively studied in theory. However, traditional methods for measuring axial motion of a string are very challenging because conventional accelerometers are difficult to install on moving objects, and lasers cannot accurately track slender and moving strings. Here we present an optical tracking technique based on computer vision for measuring the vibrations of axially moving strings. A novel multi-point, full-field optical vibration measurement method is proposed, specifically tailored for this experimental context. High-speed cameras capture motion images of strings moving at constant axial velocities, and optical flow algorithms compute the corresponding motion displacements. Time-domain displacement data from these measurements are then transformed into amplitude-frequency information via Fourier transform. Vibration signals are further analyzed using the poly-reference least-squares complex frequency domain estimation method to extract stable natural frequencies and mode shapes of the lateral vibrations. Comparison with theoretical results demonstrates the method’s high computational accuracy.