Semi-Analytical Finite Element method for guided waves in civil engineering plate-like structures

Abstract: Guided waves have a signicant potential for Structural Health Monitoring (SHM) and Non-Destructive Testing (NDT) due to their relatively long distance of propagation and sensitivity to discontinuities along the propagation path, anywhere through the material thickness. The inability to model wave guides of arbitrary cross-section using current matrix methods, has led to the development of a technique called Semi-Analytical Finite Element (SAFE). In civil engineering it is of considerable interest to study guided waves in plates and plate-like structures: such as foundations, embankments, reactor enclosures and dams. NDT have potential as an essential tool in the life cycle management of the built environment: from preliminary investigations, verication of new structures to its maintenance and, nally, demolition. In this master's thesis the semi-analytical nite element method is reviewed, implemented and studied for civil engineering plate-like structures using the commercial nite element software COMSOL. First, a review of SAFE and its underlying concepts, such as solid mechanics, Lamb waves and quadratic eigenvalue problems, is presented. Second, its implementation, using a coecient form Partial Dierential Equation (PDE) formalism in COMSOL's mathematical modelling environment, is presented. Third, SAFE is applied to four civil engineering problems: (1) a continuous homogeneous isotropic linear elastic free plate, (2) a continuous homogeneous isotropic linear elastic free plate with proportional hysteretic damping, (3) a continuous isotropic linear elastic free plate with a stiness gradient and (4) a multi-layered half-space. The SAFE model solution is curve tted to synthetic data from the matrix method software DISPERSE. 3 It is found that SAFE successfully predicts the dispersion relations for the enumerated civil engineering structures. Furthermore, it is shown that exploiting the underlying eigenvalues and eigenvectors, extended properties such as attenuation, lossless excitability and energy velocity may be predicted using a SAFE formulation. Moreover, it is shown that introducing light damping to a free plate results in negligible changes in phase velocities. Furthermore, it is shown that a stiness gradient over the plate thickness have small eects on the S1 zero group velocity frequency.