KEYWORDS: Waveguides, Signal attenuation, Chemical elements, Dispersion, 3D modeling, Computer simulations, Wave propagation, Finite element methods, Water, Acoustics
Vibroacoustic three-dimensional finite element simulations are performed to validate a novel formulation that
model leaky guided waves properties for waveguides surrounded by fluids. The above formulation couples a mesh
of semi-analytical finite elements (SAFE), to discretize the waveguide cross-section, with a mesh of boundary
elements (BEM) to model the unbounded outer fluid domain. The resulting dispersion curves are validated
through dedicated finite element simulations where the extracted time-transient waveforms are analyzed via a
modified Matrix Pencil Method in time and space. Wave simulations are achieved using ABAQUS/Explicit for
an elastic steel bar of square cross section immersed in water and the results obtained are compared with those
given by the SAFE-BEM method.
KEYWORDS: Bone, Wave propagation, Tissues, Waveguides, 3D modeling, Ultrasonics, Chemical elements, Magnetic resonance imaging, Finite element methods, Fourier transforms
This paper presents a dedicated Finite Element approach for quantitative time-transient simulations of stress
and pressure waves propagation in biological structures as human bones. The tool, starting from a magnetic
resonance image (MRI) as the one of a human leg, builds a three-dimensional finite element (FE) mesh by
converting voxels into elements. This step does not require any segmentation or further geometric interpretation
of the tissue structure, only the mechanical properties have to be provided via Hounsfield (HU) number density
mapping. The proposed tool improves upon the usually adopted models taking into account the irregular
geometry of the bone as well as the soft tissues and their damping role, typically neglected. The tool code
can handle models of hundred millions of elements in a standard PC desktop, exceeding thus capabilities of
commercially available FEM codes. Here, an application on a human leg is proposed to show the potential
of the proposed tool. The results of the time-transient simulations are next exploited to validate the use of
guided waves models for the non invasive ultrasonic diagnosis of elongated bones. In particular, the recorded
time-waveforms are analyzed via the 2D Fast Fourier Transform and the frequency-wavenumber energy content
of the propagating waves is extracted. Such information is compared with the guided waves dispersion curves
predicted, considering a representative cross-section of the tibia, via a Semi Analytical Finite Element (SAFE)
formulation. Some final considerations on the comparison of the extracted and predicted dispersion curves close
the paper.
The characterization of bones via axial ultrasonic transmission techniques can be fully exploited only once the
complexities of guided wave propagation are unveiled. Generally, plate/cylindrical waveguide models, where the
soft tissues and their damping role are generally neglected, are used to identify the propagating waves in the
bone. Here, a numerical strategy for a more rigorous simulation of guided wave propagation in elongated bones
is proposed. First, from a computed tomography image of a human leg a three-dimensional finite element (FE)
mesh of the problem is built by converting voxels into elements. At this level, the mechanical properties of bones
and soft tissues can be obtained converting the Hounsfield units. If necessary, the FE mesh can be enhanced
by smoothing the outer surfaces of the bone and/or skin. Next, time-transient three-dimensional explicit FE
simulations are performed to simulate the propagation of stress waves along the bone with and without the soft
tissues. The propagative energy is revealed by processing the bone time-responses with a 2D-FFT transform
suitable for guided waves extraction. Finally, a representative bi-dimensional cross-section of the bone only is
used to set the guided wave equation by means of a Semi-Analytical Finite Element (SAFE) formulation. Via
SAFE, the dispersion curves are obtained and compared with the 2D-FFT energy map. The proposed strategy
can support the research on non-invasive techniques based on stress waves for the assessment of long bones.
High tensile strength steel strands are widespread load carrying structural components in civil structures. Due to
their critical role, several researchers have investigated nondestructive techniques to assess the presence of damage such
as corrosion or the change in prestress level (prestress loss). Ultrasonic Guided Waves are known to be an effective
approach for defect detection in components with waveguide geometry such as strands. However, Guided Wave
propagation (dispersion properties) in steel strands is fairly complex partially due to the strand helical geometry and the
influence of axial prestress. For instance, the strand axial stress generates a proportional radial stress between adjacent
wires (interwire stress) that is responsible for inter-wire coupling effects.
While experimental and numerical investigations have attempted to study and predict wave propagation in axially
loaded strands, the propagation phenomenon is not yet fully understood. The present paper intends to improve the
knowledge of dispersion properties in progressively loaded seven wire strands accounting for helical geometry and interwire
contact forces. Full three dimensional Finite Element simulations as well as Semi-Analytical Models will be used to
predict the dispersion curves in strands as a function of the axial stress.
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