A vibration-testing framework for detecting and identifying failing joints between composite structural members without dedicated equipment (accelerometers, amplifiers) or time-consuming system modeling methods is introduced. The sensing element is a 2826MB Metglas® magnetoelastic strip embedded in one of the members during its 3D-printing (layer-by-layer) fabrication process in fused deposition modeling mode. External dynamic loading of the structure causes changes to the strip’s magnetization, thus inducing voltage to a nearby placed coil in a contactless manner. The resulting signal depends on the structure’s behavior under loading (and therefore its condition), and may be recorded without amplification or filtering by conventional oscilloscopes. Its frequency analysis reveals patterns of shifted frequency and/or altered damping at specific modes attributed to failing joints. Apart from yielding results using less dedicated equipment than other vibration-testing methods, the current framework offers two additional benefits: (i) Excitation may be applied to the same structural point for all monitored joints; (ii) estimation of damping values for a given mode does not have to rely on empirical or system modelling techniques (both requiring dedicated expertise). Test runs with structures formed by two or three composite slabs joined in-series indicate promising results with successful detection and identification of failing joints.