Structural Health Monitoring of Nonlinear Beam under Combined Translational and Rotational Vibration

Abstract

This study presents a nonlinear dynamic methodology for detecting fatigue damage precursor in an isotropic metallic cantilever beam exposed to harmonic transverse, rotation or combined ¬– transverse and rotation – base excitations. The methodology accounts for important dynamic nonlinearities due to the complex loading generated by uniaxial and multiaxial nonlinear oscillations. These nonlinearities include: 1) structural stiffening due to gyroscopic motion and high-response amplitude at the structure fundamental mode, 2) structural softening due to inertial forces and gyroscopic loads, and localized evolution in the material microstructure due to fatigue damage and 3) cross-axis coupling due to multiaxial loading. The loading intensity and number of vibration cycles intensified these nonlinearities. The damage precursor feature is acquired by quantifying the reduction in the nonlinear stiffness term in the equation of motion due to localized evolution in the material micromechanical properties at high stress concentration regions. Nanoindentation studies near high stress concentration sites confirmed the evolution in the local micromechanical properties, as a function of loading cycles. The nonlinear analytical approach tracks the degradation in the structural stiffness as a function of the nonlinear dynamic response for the uniaxial transverse or rotation base excitation. The change in the dynamic response due to damage precursor is captured experimentally. The nonlinear stiffness terms are found to be sensitive to fatigue damage precursor for translational or rotational excitation. Therefore, the nonlinear stiffness sensitivity to fatigue damage precursor appeared to be a promising metric for structural health monitoring applications. This method is applicable to a cantilever beam only. Additional investigations will be required to extend its applicability to more complex structures. For the combined transverse and rotation base excitation, the experimental and analytic results demonstrated the importance of cross-axis coupling. The Experiments are performed using a unique multiaxial electrodynamic shaker with high controllability of phase and base excitation frequencies. The analytical model captures the modulation in the nonlinear dynamic response behavior seen in the experiments as a function of cross-axis coupling and the phase relation between the axes. Although the model is successful in capturing these general trends, it does not agree with the beam deflection absolute values obtained from the experiments. The discrepancy is due to fatigue damage accumulation during the experiments, which is manifested by a shift in the resonance frequency and an increase in the response amplitude.