SUBMITTED VERSION
Reza Soleimanpour, Ching-Tai Ng and Chun H.Wang
Higher harmonic generation of guided waves at delaminations in laminated composite
beams
Structural Health Monitoring, 2017; 16(4):400-417
© The Author(s) 2016
Published version available via DOI: http://dx.doi.org/10.1177/1475921716673021
http://hdl.handle.net/2440/107034
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11 February 2020
date ‘rights url’ accessed / permission obtained: (overwrite text)
1
Higher harmonic generation of guided waves at delaminations in
laminated composite beams
Reza Soleimanpour
1
, Ching-Tai Ng
1,*
and Chun Wang
2
Abstract: Detection and characterization of delamination damage is of great importance
to the assurance of structural safety. The present work investigates the potential of a
baseline-free structural health monitoring technique based on higher harmonics
resulting from the nonlinear interaction of guided wave and a delamination. The
nonlinearity considered in this study arises from the clapping of the sub-laminates in the
delaminated region, which generates contact acoustic nonlinearity (CAN). Both explicit
finite element (FE) simulations and experimental tests are conducted on composite
laminates containing a delamination of different sizes and at different through-thickness
locations. The results show that the interaction between the fundamental asymmetric
mode (A
0
) of guided wave and a delamination generates CAN in the form of higher
harmonics, which provides a good measure for identifying the existence of
delaminations and determining their sizes in laminated composite beams. This new
1
School of Civil, Environmental & Mining Engineering, The University of Adelaide,
SA, Australia
2
School of Mechanical and Manufacturing Engineering, University of New South
Wales (UNSW), Sydney, Australia
Corresponding author:
* Ching-Tai Ng, School of Civil, Environmental & Mining Engineering, The University
of Adelaide, SA, Australia
Email: alex.ng@adelaide.edu.au
2
insight into the generation mechanisms of nonlinear higher order harmonics in
composite laminates will enhance the detection and monitoring of damage in composite
structures.
Keywords
Contact acoustic nonlinearity, delamination, fiber reinforced laminated composite beam,
finite element, nonlinear guided waves.
Introduction
Damage detection is essential to structural integrity management of engineered
structures on which human safety depends. Structural health monitoring techniques
employing guided waves and distributed sensors have shown promises in
complementing existing non-destructive evaluation (NDE) techniques, such as
radiography, electro-mechanical impedance based, eddy current technique, visual
inspection, shearography, thermography and conventional ultrasonic [1]. Compared to
conventional NDE techniques, guided waves techniques [2-4] offer several major
advantages, such as the ability to inspect inaccessible locations and large areas
autonomously, without interrupting operations [5-9]. However, guided wave methods
require subtracting the wave data of the un-damaged state (baseline data) from the total
wave to obtain the scattered wave data attributed to damage [10,11]. Recently nonlinear
ultrasonic phenomenon is emerging as a new concept to alleviate the need for baseline
data by exploiting side bands and higher harmonics that are generated only by the
clapping and/or friction between the faces of a crack subjected to an incident wave.
3
When a single-frequency guided wave encounters a linear structural feature, such as a
hole or a stiffener, the scattered waves is of the same frequency as the original wave.
However, additional frequencies can be generated by geometrically nonlinear structural
features such as breathing cracks whose surfaces come into contact [12], or material
nonlinearity [13,14]. Examples of these nonlinear acoustical phenomena include (a)
higher harmonic generation, (b) sub-harmonic generation, (c) nonlinear resonance and
(d) mix frequency response. Among these, higher order harmonic generation and
frequency mixing have been commonly used as indicators of acoustic nonlinearities.
Basically the non-linear acoustic phenomena involve classical and non-classic
responses. The classical non-linear response is mostly concerned with material
imperfections such as intrinsic nonlinearities due to imperfections in atomic lattices
leading to higher harmonic generation. Localized fatigue cracks, distributed micro-
cracks or other material imperfections are some of the sources of classical non-linear
response. Research work in this area also involves higher harmonic generation of Lamb
waves used for the detection of material nonlinearity and damage.
Classical nonlinear effects in guided waves propagation have been investigated by many
researchers and explored for damage detection. Deng [15,16] investigated the
generation of second harmonic of shear horizontal waves and Lamb waves in metallic
plates. Müller et al. [17] investigated the characteristics of second harmonic generation
of Lamb wave in a plate with quadratic nonlinearity. Liu et al. [13] investigated the
symmetry properties of second harmonic Lamb waves by examining anti-symmetric
Lamb mode pairs. Zhang et al. [18] reported the observation of cumulative second
harmonic generation of Lamb wave in long bones based on the modal expansion
4
approach to waveguide excitation and the dispersion characteristics of Lamb waves in
long bones. It was shown that the second-harmonic signal generated by fundamental
Lamb waves in long bones is observed clearly, and the effect is cumulative with
propagation distance when the fundamental Lamb wave mode and its second harmonic
mode have the same phase velocities. Xiang et al. [19] developed an analytical model
for the effect of the interactions of dislocations with precipitate coherency strains on the
generation of second harmonic of Lamb waves in metallic alloys. Lissenden et at. [20]
studied generation of higher harmonics of guided waves in aluminum plates with plastic
deformation. It was shown that plastic deformation has a significant effect on the
harmonic amplitude ratio. Pruell et al. [21] studied the generation of nonlinear guided
waves by fatigue crack in metallic plates. It was shown that the phase and group
velocity matching is essential for practical generation of nonlinear guided waves. A
technique was developed for quantitatively assessing fatigue damages in metallic plates
based on nonlinear guided waves. Bermes et al. [22] developed a procedure to
determine the second harmonic of the Lamb waves in metallic plates. Srivastava and
Lanza di Scalea [23] theoretically studied the symmetry characteristics of Rayleigh–
Lamb guided waves in nonlinear, isotropic plates. It was shown that antisymmetric
motion is prohibited at all the higher order even harmonics whereas all the higher order
odd harmonics allow both symmetric and antisymmetric motions.
In contrast to classical nonlinear response, the non-classical non-linear response mostly
arises in contact-type defects in material. Crack-wave interactions that exhibit vibro-
acoustic modulations, sub-harmonic generation or stress-strain hysteresis are some of
the sources of non-classical nonlinear responses.
