Active Vibration-Based Structural Health Monitoring of CFRP Beams and Plates Using an Elastoplastic Hysteresis Model of the Nonlinear Resonant Response

An active vibration-based methodology for structural health monitoring of polymer-matrix composites is presented, in which piezoelectric actuators excite resonant vibrations and the diagnostic information is carried by two nonlinear characteristics: the backbone curve and the amplitude-dependent logarithmic decrement. Both are described by a single elastoplastic model of the Iwan (microplasticity) type with a power-law distribution of yield thresholds. The two characteristics share a common power-law exponent, and the model predicts a parameter-free ratio between the modulus defect and the hysteretic intensity. The four parameters are identified by a joint Bayesian fit. The methodology is applied to two carbon-fiber-reinforced polymer objects: a cantilever beam with a symmetric stacking sequence (three modes, 87 to 1431 Hz) and a plate strip with an unsymmetric one (two modes near 34 and 203 Hz), each tested intact and after controlled local damage. The measured ratio reproduces the prediction within 4 to 12%; whereas, the fundamental plate mode reveals a non-frictional, matrix-dominated dissipation. Local damage increases the hysteretic intensity 1.4 to 2.3 times and the modulus defect up to 2.7 times, while the resonant frequency changes by less than 0.8% and the background decrement remains nearly unchanged, giving a compact damage signature with minimal baseline requirements.