Visualization and Identification of Nonlinear Structural Dynamics Via Phase-Based Motion Magnification

The identification and analysis of nonlinear dynamics in structural systems remain critical challenges in engineering, particularly when subtle vibrational phenomena are involved. Phase-Based Motion Magnification (PBMM) has emerged as a powerful noncontact technique for visualizing fine-scale motions in complex systems, yet its application to nonlinear structural behavior remains underexplored. This study investigates the dynamic response of a beam–spring system with intentional nonlinearities, focusing on the characterization of superharmonic components and mode shapes using PBMM. Experimental tests under force-controlled stepped-sine excitation reveal pronounced hardening effects at the first resonant frequency, attributed to the geometric nonlinearity of the spring, and minimal nonlinear behavior at the second resonant frequency. High-speed video recordings were processed with PBMM, enabling the visualization of subtle energy redistribution into higher harmonics and the extraction of mode shapes across multiple frequency ranges. To enhance structural boundary visualization, a novel Visualization of Edge Detection (VED) method combining DexiNed edge detection and bilateral filtering was employed. Comparisons between PBMM results and accelerometer data validated the effectiveness of this approach in capturing nonlinear responses. These findings highlight the potential of PBMM, combined with advanced post-processing techniques, to revolutionize non-contact modal analysis and provide new insights into the nonlinear dynamics of engineering structures.