Second harmonic generation in composites: Theoretical and numerical analyses

Abstract

Second harmonic generation in a transversely isotropic plate and a symmetric composite laminate is analyzed from a theoretical perspective. The strain energy function for a nonlinear elastic transversely isotropic material is expressed in terms of the five invariants of the Green-Lagrange strain tensor. Internal resonance conditions for the generation of cumulative second harmonics indicate that a cumulative second harmonic exists when the primary-secondary mode pair satisfies the phase matching and non-zero power flux criteria. In particular, for transversely isotropic plates, when the primary mode propagates along the material principal direction, only symmetric second harmonic Lamb-like wave modes can be cumulative. Also, when the primary wave propagates along other directions, only symmetric second harmonic modes can be generated. Additionally, for the case of symmetric composite laminates, only symmetric modes can be generated as cumulative second harmonics regardless of the propagation direction of the primary mode. To validate the above theoretical predictions, finite element simulations were conducted for mode pairs that are: (i) phase matched but have zero power flux, (ii) not phase matched but have non-zero power flux, and (iii) internally resonant i.e., satisfying both phase matching and non-zero power flux criterion. The results obtained from the simulations corroborate the theoretical findings for both transversely isotropic plates and symmetric composite laminates.

Locating delaminations in laminated composite beams using nonlinear guided waves

“…Early developments on the use of the higher harmonics generated by CAN focused on determining the existence of the defects in the structures. In recent years, significant progress has been made towards using higher harmonic guided waves for damage detection, which demonstrated the feasibility of using them for detecting plastic strain, fatigue damage, micro-cracking and other types of material damages [44][45][46][47][48][49][50].…”

“…They showed that the relative acoustic nonlinearity parameter increases proportionally with the wave propagation distance due to the geometric and materials nonlinearities. Zhao et al [48] studied the second harmonic generation of Lamb waves in transversely isotropic plate and a symmetric composite laminate. They showed that for transversely isotropic plate, when waves propagate along material principal directions, the symmetric second harmonic Lamblike waves modes can be generated whereas for propagation direction other than material principal direction only the symmetric second harmonic waves are generated.…”

Propagation of Non-Linear Lamb Waves in Adhesive Joint with Micro-Cracks Distributing Randomly

“…Their results indicated that the efficiency of second harmonic generation is closely dependent on the interfacial properties. Zhao et al [39] investigated the second harmonic generation in composites and indicated that the phase matching and nonzero power flux criteria are necessary conditions for cumulative second harmonic existence, and only symmetric modes can be generated as cumulative second harmonics for symmetric composite laminates, regardless of the propagation direction of the primary mode.…”

Experimental Investigation of Second-Harmonic Lamb Wave Generation in Additively Manufactured Aluminum

“…Several studies on second-harmonic generation have been experimentally and computationally validated for inspecting microstructural damage, dislocations and persistent slips bands, as a function of plastic strain, fatigue life/cycle and propagating distance in metallic materials [8,[14][15][16][17][20][21][22][23][31][32][33]. More recent studies have investigated second-harmonic generations in composite structures [34][35][36] and cumulative third-and higher-order harmonics [6,7,37]. Furthermore, comprehensive reviews by Matlack et al [38] and Chillara and Lissenden [39] have summarized previous decades of work on the theoretical, experimental, and computational studies on nonlinear cumulative higher-order waves for nondestructive evaluation (NDE).…”