Author: Jürg Dual
To ensure the safety and reliability of a component in any mechanical device,
the mechanical properties of the material which can be anisotropic and the
number, size and distribution of faults must be tested. Especially in "new
materials" such as fibre-reinforced composites non-destructive evaluation
is not a trivial question. If the structure is "thin" in one or two
directions, i.e. if it is a rod, plate, shell etc., the application of
"structural waves" (where the wavelengths are large compared to the
characteristic dimension of the structure, i.e. the diameter of the rod or the
thickness of the plate or shell) is a method of non-destructive testing and
evaluation which offers some advantages with respect to more conventional
methods such as ultrasonics.
Detection by the Scattering Analysis of Flexural Waves
Research group: Mahir Behar Sayir
A common aircraft maintenance problem is the development of fatigue cracks
during the service life span. The fuselage and wings of planes consist of large
plate-like parts, connected with lines of rivets and fasteners. Due to the
stress concentration at these connections, fatigue cracks start to grow from the
fastener holes, and must be detected before reaching a critical length. An
elegant and promising approach is the use of guided waves, propagating along the
structure and performing such checks automatically over large parts of the
structure with a fast and cost-effective method.
Flexural waves in plates are generated using piezoelectric transducers. The
scattered field on a measurement grid around a hole is measured pointwise using
a heterodyne laser interferometer. Amplitude and phase of the scattered field
are extracted from the measured time series using fast Fourier transform. Good
agreement between the measurements and analytical calculations of the scattered
field at a circular hole is found.
measured scattered field around the hole changes significantly with the presence
of a notch or a crack, much smaller than the wavelength. This change in the
measured amplitude is modeled using finite difference methods and good agreement
is found. The significant change in amplitude due to a defect at the hole allows
the use of the proposed method for the nondestructive testing of large
structures. A flexural wave traveling along the structure can be excited, and
its scattering measured. From changes in the measured amplitudes, the
development of defects, like fatigue cracks in aircraft structures, can be
detected. As a first application, the development of fatigue cracks in tensile
specimens is monitored.
Wood is an inhomogenous cylindrical orthotropic material with
fibers in longitudinal direction. A general cylindrical orthotropic material has
nine independent material parameters: elasticity-module, shear-module and
Poisson number in longitudinal, radial and tangential directions.
Using structural waves with wavelengths larger than the
inhomogeneities and the cross-section of the beam, the global stiffness of the
structure is obtained nondestructively. We perform the following experiment
(Fig. below): A transducer produces bending (or longitudinal) waves in a wood
beam. We measure the velocity of the motion at n points perpendicularly
(or at angles of 45 degrees) to the axis of the beam.
A Fast Fourier Transform is applied to obtain a frequency
spectrum. Using a Linear Prediction Method for each frequency, we could
determine a dispersion curve (Fig. below). To extract the material properties
from the measurement, the parameters of the theoretical dispersion curve are
fitted to the experimental points, using a Least Square Algorithm. The nonlinear
equations are solved by Newton-Raphson Method.
With bending waves we could determine the elasticity-module
in longitudinal direction and the shear-module in radial and tangential
directions. Using longitudinal waves the elasticity-module in the longitudinal
direction and the Poisson numbers in the radial and in the tangential directions
are determined. It is intended to measure the elasticity-module in the radial,
and the shear-module in the longitudinal directions. For this experiment a
wooden plate in paralell with fibers is needed.
of Defects in Cylindrical Structures
Research group: Jürg Dual
The detection and characterization of defects in structures is an important
issue in non-destructive testing. To avoid the scanning of large samples, guided
elastic waves, which propagate along the structure are excited at one end. These
waves interact with a defect, which results in a scattered wave field. In a
first step, the displacements of these scattered waves are recorded over time at
different circumferential positions in an experiment. The first figure shows the
Laserinterferometer setup, which is used to measure the three displacement
Then these measured displacement histories are reversed in time and used as
displacement excitations of the corresponding points in a simulation. As long as
the geometric and material parameters are chosen equivalent to the performed
experiment, the scattered waves travel back through the simulated structure and
interfere at the position of the defect, even if no defect is present in the
numerical model (see second figure).
Wave Propagation in Cylindrical Structures
Author: Daniel Gsell
Research group: Jürg Dual
Guided wave propagation in cylindrical, anisotropic structures is studied in
a frequency range up to 1 MHz. The investigations are carried out with carbon
fibre reinforced tubes. The emphasis is the experimental determination of their
linear elastic material properties.
The wavelengths of axially propagating waves at certain frequency are
influenced considerably by the elastic material parameters. This dependency is
used in order to determine the material properties experimentally, by the
solution of the inverse problem. In the experiment the surface displacements of
travelling waves are measured along the axis of the tube with a laser
interferometer. The extraction of the dispersion curves is achieved by a
signal-processing algorithm based on a Fourier transformation in time and on a
Matrix-Pencil algorithm in space-domain.
Figure 1: Influence of the variation of a
stiffnesselement (+/- 10% and 20%) on the dispersion relation of a carbon fibre
reinforced tube, pipe mode n = 2.
For the theoretical description of the dispersion relation we avail ourselves
of a numerical-analytical procedure, which is based on the Hamilton' principle.
In time, tangential and axial direction global, trigonometric functions are used
while in radial direction the problem is discretized and approximated by finite
elements. The solution of the inverse problem is done with the method of total
least squares. To obtain a robust optimization algorithm with respect to
outliers in the input data, the residues are used to classify the data points
into in- and outliers.
In order to test and validate the present method systematically, artificially
generated data are used. Therefore, the wave propagation in the tube, as well as
the piezoelectric excitation are simulated with the finite-difference method in
time domain. As a by-product the developed tool can be used for the
visualization of the wave propagation in anisotropic tubes and contributes to
the understanding of these complex phenomena.
Figure 2: Wave propagation in an anisotropic tube excited
by a point source. a) axial, b) radial, and c) tangential surface displacement.
Laser-based Ultrasonics at the Nanometer Scale
Authors: Dieter M.
Profunser, Jacqueline Vollmann
Research group: Jürg Dual
on page Micro- and Nanomechanics