Development of a new isogeometric finite element and its application for Lamb wave based structural health monitoring

Magdeburg, Univ., Fak. für Maschinenbau, Diss., 2012

Lamb mode diversity imaging for non-destructive testing of plate-like structures

Several Lamb wave modes can be coupled to a particular structure, depending on its geometry and transducer used to generate the guided waves. Each Lamb mode interacts in a particular form with different types of defects, like notches, delamination, surface defects, resulting in different information which can be used to improve damage detection and characterization. An image compounding technique that uses the information obtained from different propagation modes of Lamb waves for non-destructive testing of plate-like structures is proposed. A linear array consisting of 16 piezoelectric elements is attached to a 1 mm thickness aluminum plate, coupling the fundamental A0 and S0 modes at the frequencies of 100 kHz and 360 kHz, respectively. For each mode two images are obtained from amplitude and phase information: one image using the Total Focusing Method (TFM) and one phase image obtained from the Sign Coherence Factor (SCF). Each TFM image is multiplied by the SCF image of the respective mode to improve contrast and reduce side and grating lobes effects. The high dispersive characteristic of the A0 mode is compensated for adequate defect detection. The information in the SCF images is used to select one of the TFM mode images, at each pixel, to obtain the compounded image. As a result, dead zone is reduced, resolution and contrast are improved, enhancing damage detection when compared to the use of only one mode. © 2013 Elsevier Ltd.

Lamb mode diversity imaging fornon-destructivetesting of plate-likestructures

Several Lamb wave modes can be coupled to a particular structure, depending on its geometry and transducer used to generate the guided waves. Each Lamb mode interacts in a particular form with different types of defects, like notches, delamination, surface defects, resulting in different information which can be used to improve damage detection and characterization. An image compounding technique that uses the information obtained from different propagation modes of Lamb waves for non-destructive testing of plate-like structures is proposed. A linear array consisting of 16 piezoelectric elements is attached to a 1 mm thickness aluminum plate, coupling the fundamental A0 and SO modes at the frequencies of 100 kHz and 360 kHz, respectively. For each mode two images are obtained from amplitude and phase information: one image using the Total Focusing Method (TFM) and one phase image obtained from the Sign Coherence Factor (SCF). Each TFM image is multiplied by the SCF image of the respective mode to improve contrast and reduce side and grating lobes effects. The high dispersive characteristic of the A0 mode is compensated for adequate defect detection. The information in the SCF images is used to select one of the TFM mode images, at each pixel, to obtain the compounded image. As a result, dead zone is reduced, resolution and contrast are improved, enhancing damage detection when compared to the use of only one mode. (C) 2013 Elsevier Ltd. All rights reserved. (AU)

Modelling of Lamb waves in composite laminated plates excited by interdigital transducers

The technique of permanently attaching interdigital transducers (IDT) to either flat or curved structural surfaces to excite single Lamb wave mode has demonstrated great potential for quantitative non-destructive evaluation and smart materials design, In this paper, the acoustic wave field in a composite laminated plate excited by an IDT is investigated. On the basis of discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the surface velocity response of the plate due to the IDTs excitation. In this approach, the frequency spectrum and wave number spectrum of the output of IDT are obtained directly. The corresponding time domain results are calculated by applying a standard inverse fast Fourier transformation technique. Numerical examples are presented to validate the developed method and show the ability of mode selection and isolation. A new effective way of transfer function estimation and interpretation is presented by considering the input wave number spectrum in addition to the commonly used input frequency spectrum. The new approach enables the simple physical evaluation of the influences of IDT geometrical features such as electrode finger widths and overall dimension and excitation signal properties on the input-output characteristics of IDT. Finally, considering the convenience of Mindlin plate wave theory in numerical computations as well as theoretical analysis, the validity is examined of using this approximate theory to design IDT for the excitation of the first and second anti-symmetric Lamb modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Single mode Lamb waves in composite laminated plates generated by piezoelectric transducers

The technique of permanently attaching piezoelectric transducers to structural surfaces has demonstrated great potential for quantitative non-destructive evaluation and smart materials design. For thin structural members such as composite laminated plates, it has been well recognized that guided Lamb wave techniques can provide a very sensitive and effective means for large area interrogation. However, since in these applications multiple wave modes are generally generated and the individual modes are usually dispersive, the received signals are very complex and difficult to interpret. An attractive way to deal with this problem has recently been introduced by applying piezoceramic transducer arrays or interdigital transducer (IDT) technologies. In this paper, the acoustic wave field in composite laminated plates excited by piezoceramic transducer arrays or IDT is investigated. Based on dynamic piezoelectricity theory, a discrete layer theory and a multiple integral transform method, an analytical-numerical approach is developed to evaluate the input impedance characteristics of the transducer and the surface velocity response of the plate. The method enables the quantitative evaluation of the influence of the electrical characteristics of the excitation circuit, the geometric and piezoelectric properties of the transducer array, and the mechanical and geometrical features of the laminate. Numerical results are presented to validate the developed method and show the ability of single wave mode selection and isolation. The results show that the interaction between individual elements of the piezoelectric array has a significant influence on the performance of the IDT, and these effects can not be neglected even in the case of low frequency excitation. It is also demonstrated that adding backing materials to the transducer elements can be used to improve the excitability of specific wave modes. (C) 2002 Elsevier Science Ltd. All rights reserved.

Convectively coupled equatorial waves: A new methodology for identifying wave structures in observational data

Convectively coupled equatorial waves are fundamental components of the interaction between the physics and dynamics of the tropical atmosphere. A new methodology, which isolates individual equatorial wave modes, has been developed and applied to observational data. The methodology assumes that the horizontal structures given by equatorial wave theory can be used to project upper- and lower-tropospheric data onto equatorial wave modes. The dynamical fields are first separated into eastward- and westward-moving components with a specified domain of frequency–zonal wavenumber. Each of the components for each field is then projected onto the different equatorial modes using the y structures of these modes given by the theory. The latitudinal scale yo of the modes is predetermined by data to fit the equatorial trapping in a suitable latitude belt y = ±Y. The extent to which the different dynamical fields are consistent with one another in their depiction of each equatorial wave structure determines the confidence in the reality of that structure. Comparison of the analyzed modes with the eastward- and westward-moving components in the convection field enables the identification of the dynamical structure and nature of convectively coupled equatorial waves. In a case study, the methodology is applied to two independent data sources, ECMWF Reanalysis and satellite-observed window brightness temperature (Tb) data for the summer of 1992. Various convectively coupled equatorial Kelvin, mixed Rossby–gravity, and Rossby waves have been detected. The results indicate a robust consistency between the two independent data sources. Different vertical structures for different wave modes and a significant Doppler shifting effect of the background zonal winds on wave structures are found and discussed. It is found that in addition to low-level convergence, anomalous fluxes induced by strong equatorial zonal winds associated with equatorial waves are important for inducing equatorial convection. There is evidence that equatorial convection associated with Rossby waves leads to a change in structure involving a horizontal structure similar to that of a Kelvin wave moving westward with it. The vertical structure may also be radically changed. The analysis method should make a very powerful diagnostic tool for investigating convectively coupled equatorial waves and the interaction of equatorial dynamics and physics in the real atmosphere. The results from application of the analysis method for a reanalysis dataset should provide a benchmark against which model studies can be compared.

Equatorial Kelvin waves as revealed by EOS Microwave Limb Sounder observations and European Centre for Medium-Range Weather Forecasts analyses: Evidence for slow Kelvin waves of zonal wave number 3

[1] Temperature and ozone observations from the Microwave Limb Sounder (MLS) on the EOS Aura satellite are used to study equatorial wave activity in the autumn of 2005. In contrast to previous observations for the same season in other years, the temperature anomalies in the middle and lower tropical stratosphere are found to be characterized by a strong wave-like eastward progression with zonal wave number equal to 3. Extended empirical orthogonal function (EOF) analysis reveals that the wave 3 components detected in the temperature anomalies correspond to a slow Kelvin wave with a period of 8 days and a phase speed of 19 m/s. Fluctuations associated with this Kelvin wave mode are also apparent in ozone profiles. Moreover, as expected by linear theory, the ozone fluctuations observed in the lower stratosphere are in phase with the temperature perturbations, and peak around 20–30 hPa where the mean ozone mixing ratios have the steepest vertical gradient. A search for other Kelvin wave modes has also been made using both the MLS observations and the analyses from one experiment where MLS ozone profiles are assimilated into the European Centre for Medium-Range Weather Forecasts (ECMWF) data assimilation system via a 6-hourly 3D var scheme. Our results show that the characteristics of the wave activity detected in the ECMWF temperature and ozone analyses are in good agreement with MLS data.

Multi-mode approximations to wave scattering by an uneven bed

Approximations to the scattering of linear surface gravity waves on water of varying quiescent depth are Investigated by means of a variational approach. Previous authors have used wave modes associated with the constant depth case to approximate the velocity potential, leading to a system of coupled differential equations. Here it is shown that a transformation of the dependent variables results in a much simplified differential equation system which in turn leads to a new multi-mode 'mild-slope' approximation. Further, the effect of adding a bed mode is examined and clarified. A systematic analytic method is presented for evaluating inner products that arise and numerical experiments for two-dimensional scattering are used to examine the performance of the new approximations.

Impact of non-hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow

The orographic gravity wave drag produced in flow over an axisymmetric mountain when both vertical wind shear and non-hydrostatic effects are important was calculated using a semi-analytical two-layer linear model, including unidirectional or directional constant wind shear in a layer near the surface, above which the wind is constant. The drag behaviour is determined by partial wave reflection at the shear discontinuity, wave absorption at critical levels (both of which exist in hydrostatic flow), and total wave reflection at levels where the waves become evanescent (an intrinsically non-hydrostatic effect), which produces resonant trapped lee wave modes. As a result of constructive or destructive wave interference, the drag oscillates with the thickness of the constant-shear layer and the Richardson number within it (Ri), generally decreasing at low Ri and when the flow is strongly non-hydrostatic. Critical level absorption, which increases with the angle spanned by the wind velocity in the constant-shear layer, shields the surface from reflected waves, keeping the drag closer to its hydrostatic limit. While, for the parameter range considered here, the drag seldom exceeds this limit, a substantial drag fraction may be produced by trapped lee waves, particularly when the flow is strongly non-hydrostatic, the lower layer is thick and Ri is relatively high. In directionally sheared flows with Ri = O(1), the drag may be misaligned with the surface wind in a direction opposite to the shear, a behaviour which is totally due to non-trapped waves. The trapped lee wave drag, whose reaction force on the atmosphere is felt at low levels, may therefore have a distinctly different direction from the drag associated with vertically propagating waves, which acts on the atmosphere at higher levels.

Aplicação de sensor de deslocamento angular em fibra óptica para medição de concentração de líquidos via ondas acústicas guiadas

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Simulation of surface waves in porous media

We present a novel numerical algorithm for the simulation of seismic wave propagation in porous media, which is particularly suitable for the accurate modelling of surface wave-type phenomena. The differential equations of motion are based on Biot's theory of poro-elasticity and solved with a pseudospectral approach using Fourier and Chebyshev methods to compute the spatial derivatives along the horizontal and vertical directions, respectively. The time solver is a splitting algorithm that accounts for the stiffness of the differential equations. Due to the Chebyshev operator the grid spacing in the vertical direction is non-uniform and characterized by a denser spatial sampling in the vicinity of interfaces, which allows for a numerically stable and accurate evaluation of higher order surface wave modes. We stretch the grid in the vertical direction to increase the minimum grid spacing and reduce the computational cost. The free-surface boundary conditions are implemented with a characteristics approach, where the characteristic variables are evaluated at zero viscosity. The same procedure is used to model seismic wave propagation at the interface between a fluid and porous medium. In this case, each medium is represented by a different grid and the two grids are combined through a domain-decomposition method. This wavefield decomposition method accounts for the discontinuity of variables and is crucial for an accurate interface treatment. We simulate seismic wave propagation with open-pore and sealed-pore boundary conditions and verify the validity and accuracy of the algorithm by comparing the numerical simulations to analytical solutions based on zero viscosity obtained with the Cagniard-de Hoop method. Finally, we illustrate the suitability of our algorithm for more complex models of porous media involving viscous pore fluids and strongly heterogeneous distributions of the elastic and hydraulic material properties.

Spin-Dynamics in Cold Gases of 87Rb and Atomic Hydrogen. The spins they are a-changin’

In this thesis the dynamics of cold gaseous atoms is studied. Two different atomic species and two different experimental techniques have been used. In the first part of the thesis experiments with Bose-Einstein condensates of Rb-87 are presented. In these experiments the methods of laser cooling and magnetic trapping of atoms were utilized. An atom chip was used as the experimental technique for implementation of magnetic trapping. The atom chip is a small integrated instrument allowing accurate and detailed manipulation of the atoms. The experiments with Rb-87 probed the behaviour of a falling beam of atoms outcoupled from the Bose-Einstein condensate by electromagnetic field induced spin flips. In the experiments a correspondence between the phases of the outcoupling radio frequency field and the falling beam of atoms was found. In the second part of the thesis experiments of spin dynamics in cold atomic hydrogen gas are discussed. The experiments with atomic hydrogen are conducted in a cryostat using a dilution refrigerator as the cooling method. These experiments concentrated on explaining and quantifying modulations in the electron spin resonance spectra of doubly polarized atomic hydrogen. The modifications to the previous experimental setup are described and the observation of electron spin waves is presented. The observed spin wave modes were caused by the identical spin rotation effect. These modes have a strong dependence on the spatial profile of the polarizing magnetic field. We also demonstrated confinement of these modes in regions of strong magnetic field and manipulated their spatial distribution by changing the position of the field maximum.