Energy localization and eigenvalue veering induced by local constraints in bolted structures

Vibrational energy localization, commonly attributed to disorder, periodic defects or weak coupling, can also arise from internal geometric constraints in continuous elastic systems such as those introduced in bolted connections. We investigate how the placement of an internal elastic interface within a segmented beam induces eigenvalue veering and spatial energy confinement. A spectral model based on Euler–Bernoulli beam theory is developed, incorporating a tunable dimensionless interface parameter to represent variable constraint positioning. Furthermore, an energy-based localization metric reveals confinement regions and tracks modal exchanges across veering regions. The theoretical predictions are validated experimentally using non-contact laser Doppler vibrometry (LDV) on a geometrically tunable bolt–nut assembly. Results confirm that the local constraint can be used to understand vibrational spectra and induce strong localization. These results position internal constraint geometry as a practical tuning mechanism for shaping vibrational spectra in continuous elastic systems, with direct relevance to bolted connections, and provide new opportunities for engineered mode control in structural joints and segmented media.