Phase Influence of Combined Rotational and Transverse Vibrations on the Structural Response

The planar dynamic response of a cantilever metallic beam structure under combined harmonic base excitations (consisting of in-plane transverse and rotation about the out-of-plane transverse axis) was investigated experimentally. The important effect of the phase angle between the two simultaneous biaxial excitations on the beam tip displacement was demonstrated. The experiments were performed using a unique six degree-of-freedom (6-DoF) electrodynamic shaker with high control accuracy. The results showed that the beam tip displacement at the first flexural mode was amplified when the phase angle between the rotational and translational base excitations was increased. The beam nonlinear stiffness, on the other hand, simultaneously: (i) decreased due to fatigue damage accumulation, and (ii) increased due to an increase in the phase angle. The results were compared to the uniaxial excitation technique, where the principle of superposition was applied (mathematical addition of the structural response for each uniaxial excitation). The principle of superposition was shown to overestimate the structural response for low phase angles. Thus, the application of the superposition vibration testing as a substitute for multiaxial vibration testing may lead to over-conservatism and erroneous dynamic and reliability predictions.