Non-collinear interaction of guided elastic waves in an isotropic plate

Abstract

The nonlinear wave propagation in a homogeneous and isotropic elastic plate is analyzed theoretically to investigate the non-collinear interaction of plate wave modes. In the presence of two primary plate waves (Rayleigh-Lamb or shear horizontal modes) propagating in arbitrary directions, an explicit expression for the modal amplitude of nonlinearly generated wave fields with the sum or difference frequency of the primary modes is derived by using the perturbation analysis. The modal amplitude is shown to grow in proportion with the propagation distance when the resonance condition is satisfied, i.e., when the wavevector of secondary wave coincides with the sum or difference of those of primary modes. Furthermore, the non-collinear interaction of two symmetric or two antisymmetric modes is shown to produce the secondary wave fields consisting only of the symmetric modes, while a pair of symmetric and antisymmetric primary modes is shown to produce only the antisymmetric modes. The influence of the intersection angle, the primary frequencies, and the mode combinations on the modal amplitude of secondary wave is examined for a low-frequency range where the lowest-order symmetric and antisymmetric Rayleigh-Lamb waves and the lowest-order symmetric shear horizontal wave are the only propagating modes.

Nonlinear Guided-Wave Mixing for Condition Monitoring of Bolted Joints

“…Given the multimodal nature of guided waves, and the existence of higher-order propagation modes, limited work in the field of nonlinear guided-wave mixing can be found in the literature, aiming at fundamentally understanding the mixing phenomenon as in [ 32 , 33 , 34 , 35 ] and some types of damage-related mechanisms [ 36 , 37 , 38 ]. Croxford et al [ 39 ] investigated material degradation detection using wave mixing, and Jingpin et al investigated the use of wave mixing to detect fatigue crack [ 40 ] and thermal corrosion [ 41 ] damage in steel specimens.…”

Experimental and Numerical Investigation of the Micro-Crack Damage in Elastic Solids by Two-Way Collinear Mixing Method

“…Hu et al [ 30 , 31 ] investigated the one-way collinear mixing of A 0 and S 0 mode Lamb waves with quadratic nonlinearity and randomly distributed micro-cracks. In addition, the non-collinear ultrasonic wave mixing technique [ 32 , 33 , 34 , 35 , 36 , 37 ] has also been studied by some researchers. Xiang [ 36 ], Croxford [ 38 ], Mao [ 39 ] and Jiao et al [ 40 , 41 ] employed non-collinear two shear waves mixing method to detect plasticity, fatigue and a single fatigue crack.…”

“…Xiang [ 36 ], Croxford [ 38 ], Mao [ 39 ] and Jiao et al [ 40 , 41 ] employed non-collinear two shear waves mixing method to detect plasticity, fatigue and a single fatigue crack. Ishii et al [ 34 , 42 ] analytically and numerically investigated the modal amplitude in the non-collinear interaction of guided waves. Wang et al [ 43 , 44 ] proposed analytical models to predict nonlinear mixing of non-collinear guided waves and bulk waves at a contact interface, respectively.…”

Experimental and Numerical Study of Nonlinear Lamb Waves of a Low-Frequency S0 Mode in Plates with Quadratic Nonlinearity

“…However, nonlinear ultrasonic technologies [4,5,6,7,8,9,10,11,12,13,14] are dramatically sensitive to material microstructures, which could be promising in overcoming this problem. Especially nonlinear Lamb-wave detection techniques [15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39], which can be employed for long-range monitoring and inspection in thin plate structures, have attracted extensive attention in the past two decades.…”

“…Jiao et al [31] reported the application of nonlinear Lamb wave-mixing method to detect the micro-cracks in plates. Ishii et al [32] have theoretically investigated the non-collinear interaction of plate wave modes when the nonlinear wave is propagating in elastic plates. Zhao et al [33] applied one-way collinear mixing method to numerically investigate the propagation of Lamb waves in thin plates with quadratic nonlinearity.…”