Frequency sweep study on the generation of dual-mode second harmonics (DMSH) on an isotropic nonlinear elastic cylindrical rod by T(0,1) mode

Abstract

Nonlinear ultrasonic (NLU) guided wave (GW) measurements are more sensitive to microscale defects than linear measurements. This nonlinear phenomenon is helpful for early-stage damage detection in material for nondestructive evaluation (NDE) and structural health monitoring (SHM) applications. The amplitude of the higher harmonics generated in the material serves as the basis for the NLU measurement. Recent studies have reported the presence of dual-mode second harmonic (DMSH) on an isotropic nonlinear elastic plate and cylindrical structures. The fundamental non-dispersive mode shear horizontal SH0 and torsional T(0,1) modes can generate simultaneously propagating dual-mode second harmonic(DMSH) on plate and cylindrical guided media respectively. For the case of cylinders, at phase matching condition two dominant second harmonic fundamental longitudinal (l(0,1)) and orthogonal torsional (t(0,1)┴) mode are generated with significant amplitude. The particle vibration of the t(0,1)┴ mode was present in both orthogonal directions compared to conventional T(0,1) mode and hence called orthogonal torsional mode. The present work aims to study the behaviour of DMSH at different frequencies through a frequency sweep study on a weakly nonlinear elastic cylinder of circular cross-section via numerical simulations and validated experimentally for some selected cases. The wave propagation of the T(0,1) mode at several selected frequencies from 300 kHz to 2.2 MHz is chosen to explore the second harmonic mode for better understanding. At frequencies below 1.25 MHz, l(0,1) mode is faster than t(0,1)┴ mode; above 1.25 MHz, it was the other way around. The behaviour of harmonics was observed to be in accordance with the group and phase velocities at the corresponding frequencies in the dispersion curves. The evidence for the presence of DMSH was validated experimentally for some selected frequency cases at different propagation distances. The significance of DMSH is explored via numerical simulations and found that t(0,1)┴ mode is sensitive towards material degradation, while all other generated wave modes were not affected. Research shows that enough energy is available in the generated DMSH to be noticed experimentally and in numerical simulations. This improved understanding of the generation of DMSH across different frequencies would be helpful in new advanced NLU-based NDE and SHM applications.