Computation of dispersion curves for embedded waveguides using a dashpot boundary condition

Notes on osculations and mode tracing in semi-analytical waveguide modeling

The dispersion curves of (elastic) waveguides frequently exhibit crossings and osculations (also known as veering, repulsion, or avoided crossing). Osculations are regions in the dispersion diagram where curves approach each other arbitrarily closely without ever crossing before veering apart. In semi-analytical (undamped) waveguide models, dispersion curves are obtained as solutions to discretized parameterized Hermitian eigenvalue problems. In the mathematical literature, it is known that such eigencurves can exhibit crossing points only if the corresponding matrix flow (parameter-dependent matrix) is uniformly decomposable. We discuss the implications for the solution of the waveguide problem. In particular, we make use of a simple algorithm recently suggested in the literature for decomposing matrix flows. We also employ a method for mode tracing based on approximating the eigenvalue problem for individual modes by an ordinary differential equation that can be solved by standard procedures.

Defect reconstruction in a two-dimensional semi-analytical waveguide model via derivative-based optimization

This paper considers an indirect measurement approach to reconstruct a defect in a two-dimensional waveguide model for a non-destructive ultrasonic inspection via derivative-based optimization. The propagation of the mechanical waves is simulated by the scaled boundary finite element method that builds on a semi-analytical approach. The simulated data are then fitted to given data associated with the reflected waves from a defect which is to be reconstructed. For this purpose, we apply an iteratively regularized Gauss-Newton method in combination with algorithmic differentiation to provide the required derivative information accurately and efficiently. We present numerical results for three kinds of defects, namely, a crack, delamination, and corrosion. The objective function and the properties of the reconstruction method are investigated. The examples show that the parameterization of the defect can be reconstructed efficiently as well as robustly in the presence of noise.

Efficient simulation of elastic guided waves interacting with notches, adhesive joints, delaminations and inclined edges in plate structures

This paper presents an approach to model transmission and reflection phenomena of elastic guided waves in plates. The formulation is applied to plate structures containing notches, inclined edges, delaminations or (adhesive) joints. For these cases, only the thickness direction of the structure needs to be discretized at several locations, while the direction of propagation is described analytically. Consequently, the number of degrees of freedom is very small. Semi-infinite domains can be modeled, in which case the radiation condition is fulfilled exactly. Traction boundary conditions are introduced on the plate surface without requiring a mesh along the surface. Results are validated against conventional finite element implementations, showing the accuracy of the proposed approach and a reduction of the computational costs by typically 2-3 orders of magnitude.

Structural Health Monitoring of Above-Ground Storage Tank Floors by Ultrasonic Guided Wave Excitation on the Tank Wall

There is an increasing interest in using ultrasonic guided waves to assess the structural degradation of above-ground storage tank floors. This is a non-invasive and economically viable means of assessing structural degradation. Above-ground storage tank floors are ageing assets which need to be inspected periodically to avoid structural failure. At present, normal-stress type transducers are bonded to the tank annular chime to generate a force field in the thickness direction of the floor and excite fundamental symmetric and asymmetric Lamb modes. However, the majority of above-ground storage tanks in use have no annular chime due to a simplified design and/or have a degraded chime due to corrosion. This means that transducers cannot be mounted on the chime to assess structural health according to the present technology, and the market share of structural health monitoring of above-ground storage tank floors using ultrasonic guided wave is thus limited. Therefore, the present study investigates the potential of using the tank wall to bond the transducer instead of the tank annular chime. Both normal and shear type transducers were investigated numerically, and results were validated using a 4.1 m diameter above-ground storage tank. The study results show shear mode type transducers bonded to the tank wall can be used to assess the structural health of the above-ground tank floors using an ultrasonic guided wave. It is also shown that for the cases studied there is a 7.4 dB signal-to-noise ratio improvement at 45 kHz for the guided wave excitation on the tank wall using shear mode transducers.

Analyzing modal behavior of guided waves using high order eigenvalue derivatives

This paper presents a mode-tracing approach for elastic guided waves based on analytically computed derivatives and includes a study of interesting phenomena in the dispersion curve representation. Numerical simulation is done by means of the Scaled Boundary Finite Element Method (SBFEM). Two approaches are used to identify the characteristics of the resulting wave modes: Taylor approximation and Padé approximation. Higher order differentials of the underlying eigenvalue problem are the basis for these approaches. Remarkable phenomena in potentially critical frequency regions are identified and the tracing approach is adapted to these regions. Additionally, a stabilization of the solution process is suggested.

Computation of leaky guided waves dispersion spectrum using vibroacoustic analyses and the Matrix Pencil Method: a validation study for immersed rectangular waveguides

The paper aims at validating a recently proposed Semi Analytical Finite Element (SAFE) formulation coupled with a 2.5D Boundary Element Method (2.5D BEM) for the extraction of dispersion data in immersed waveguides of generic cross-section. To this end, three-dimensional vibroacoustic analyses are carried out on two waveguides of square and rectangular cross-section immersed in water using the commercial Finite Element software Abaqus/Explicit. Real wavenumber and attenuation dispersive data are extracted by means of a modified Matrix Pencil Method. It is demonstrated that the results obtained using the two techniques are in very good agreement.