KEYWORDS: Signal detection, Transducers, Aluminum, Wave propagation, Ferroelectric materials, Signal to noise ratio, Acoustics, Sensors, Signal processing, Fourier transforms
In acoustics, Lamb waves are extremely useful for damage detection in sheet materials and tubular products. Among
variety of techniques for the generation of lamb waves, lamb waves are detected using contact piezo electric transducers
mounted on an aluminum sample. For this task, two pairs of transducers were introduced where each pair mounted on
both surfaces of the sample. Mode selective excitation technique is used and two pre-amplifier circuits served as a part of
the signal detection. For this application and more precisely with low frequency excitation signal, orthogonal zero order
modes are observed in a high resolved fashion in aluminum sample of 1mm thickness. Principles of the developed
method together with instrumental details are discussed.
Based on the lattice dynamics approach the dependence of the time-of-flight (TOF) on stress has been modeled for
transversal polarized acoustic waves. The relevant dispersion relation is derived from the appropriate mass-spring model
together with the dependencies on the restoring forces including the effect of externally applied stress. The lattice
dynamics approach can also be interpreted as a discrete and strictly periodic lumped circuit. In that case the modeling
represents a finite element approach. In both cases the properties relevant for wavelengths large with respect to the
periodic structure can be derived from the respective limit relating also to low frequencies. The model representing a
linear chain with stiffness to shear and additional stiffness introduced by extensional stress is presented and compared to
existing models, which so far represent each only one of the effects treated here in combination. For a string this effect is
well known from musical instruments. The counteracting effects are discussed and compared to experimental results.
Mode selective excitation and detection together with chirped excitation and digital pulse compression is employed to
study the variation of the time-of-flight (TOF) of Lamb waves. The acoustoelastic coefficients for the variation of TOF
depend not only on the actual modes but also on the actual frequency or center frequency of the observed propagating
wave. The modes are selected from dispersion relations obtained by appropriate modeling. To allow a continuous and
monochromatic variation of the load, specially designed apparatus has been designed minimizing the disturbing
influence of static and dynamic friction, generally a demerit in the standard force exerting hydraulic equipment. The
possibility of delicate maneuverability of force application with minimal deviation with selective excitation and detection
of Lamb wave modes lead us to the observation of positive and negative acoustoelastic coefficients and dependencies of
these coefficients on applied stress with respect to central frequency are discussed.
Transducer arrangements including specially designed electronic drive and detection circuitry are presented, suitable to
distinguish between the orthogonal symmetric and anti-symmetric Lamb wave modes. Whereas transducers mounted on
both surfaces have already been introduced for this task, novel schemes based on transducers mounted single sided can also be exemplified in combination with advanced electronic schemes providing alignment with respect to the orthogonality of the separated modes. Detail of the developed scheme is exemplified together with experimental results which are compared to the expectations based on established modeling.
On the basis of first principle approaches as used for lattice dynamics basic features of the dependence of the time-offlight
of acoustic waves on elongation under stress are treated and exemplified for a linear chain. The chain is
constructed from point masses connected by mass free springs acting instantaneously. The microscopic approach is used
to exemplify the nature of the effects involved in stress or load detection by monitoring the time-of-flight of ultrasonic
waves. Whereas the effects caused by anharmonicity lead to an increase in the monitored time-of-flight, tension can also
lead to a decrease if geometric effects are present, leading to a stiffening under tension. In the absence of geometrical
stiffening, which is not present in a linear chain for longitudinal polarized waves, the time-of-flight in a harmonic chain
with forces transferred instantly is independent of tension.
Due to the dependence on a limited amount of parameters, the dispersion relations of Lamb waves can be presented in a generalized way. This is exemplified for the different established typical representations. Special attention is given to the representation of the momentum on energy, which is well suited to discuss basic features since energy as well as momentum is the properties which are strictly conserved in loss free homogeneous materials. Representations involving the phase and group velocity are discussed. Features related to level crossing of interacting modes and relations to basic mechanical properties especially relevant to Lamb waves are included in the presentation and discussion.
The detection of stress in bolts based on acoustic bulk waves of longitudinal and transversal polarization is well
introduced and respective detection schemes are commercially available. Whereas the time-of-flight of bulk waves
observed for detection varies under stress due to non-linear elastic properties, 1- or 2-dimensionally guided waves can in
addition and for suitable modes even be dominantly influenced by geometric effects. Even though geometric effects are
well known and used for example to tune string instruments, little if any attention has so far been given to similar effects
for Lamb waves and other guided modes. The basic effects including anomalous stress dependencies if compared to bulk
waves are presented and discussed including a comparison to expectations based on analytical modeling. Novel detection
schemes including developments suitable for in-flight detections of stress in structural components of aircrafts are
demonstrated.
For applications involving the determination of variations of the time-of-flight in pulsed echo or transit experiments a
method has been developed based on Fourier transformation with forced optimized compression of the reference signal
to an only bandwidth limited approximation of a Dirac-function. The respective transformation of time shifted response
signals allows the effective separation of otherwise overlapping signals and the detection of differences in the time-of-flight
for the individual components with high resolution. The developed processing scheme corrects for dispersion and
attenuation in the electronics, the transmission lines, and the transducers. The method is presented and applications are
demonstrated.
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